UPPSC AE Mechanical 13 Dec 2020 Official Paper II (Previous Year Paper)

The correct answer is option 4.

Key Points

• Gond is a tribe of Madhya Pradesh.
• Gond tribe is one of the largest Adivasi communities.
• The Gond called themselves Koi or Koiture.
• They inhabited the dense forests of the Vindhyas, Satpura and Mandla in the Narmada region of the Amarkantak range for centuries.
• Tharus is a tribe of Uttarakhand.
• They are live in Khatima and Sitarganj tehsil of UdhamSingh Nagar district (Uttarakhand).
• Todas is a tribe of Tamil Nadu.
• Todas is a tribal group in the higher altitudes of the Nilgiris.
• Santhal is a tribe of Jharkhand.
• They are also called Manjhi.
• The third-largest tribes of India are the Santhal Tribe.
• This tribe habitation is mainly in the states of West Bengal, Bihar, Odisha, Jharkhand and Assam.

Additional Information

Important tribes of :

The correct answer is September.

Key Points

• Rashtriya Poshan Maah was celebrated in September 2020.
• It was celebrated to promote nutrition among Women and Children.
• Poshan Maah is celebrated every year to encourage Jan Bhagidaari in order to ensure health and nutrition for everyone.
• Every year Poshan Maah is celebrated all over the country under POSHAN Abhiyaan, launched in 2018.
• The importance of Nutrition in our lives was emphasized by Prime Minister Shri Narendra Modi in his popular programme “Mann ki Baat” on 30th August 2020.

The correct answer is (A) - (4), (B) - (3), (C) - (2), (D) - (1).

• The highest Peak of Tamil Nadu is Doda Betta.
• The highest peak of Tamil Nadu is Doddabetta and is a part of the Nilgiri Hills at the junction of the Western Ghats as well as the Eastern Ghats.
• ​The highest peak of Rajasthan is Guru Shikhar.
• ​Guru Shikhar, a peak in the Arbuda Mountains of Rajasthan, is the highest point of the Aravalli Range. The peak is named Guru Shikhar or “peak of the guru” after Dattatreya, an incarnation of Vishnu.
• ​The highest Peak of Nagaland is Saramati.
• ​Standing at an altitude of 3841 m, Saramati is the highest peak in the state of Nagaland and occupies a place of pride in the heart of its residents.
• ​The highest peak of Madhya Pradesh is Dhoopgarh.
• The Dhupgarh Peak (1,350 metres), near Pachmarhi in south-central Madhya Pradesh, is the state's highest point.

The correct answer is Postal Service Schemes.

• The Department of Posts launched a scheme called Five Star Villages.
• It is to ensure universal coverage of flagship postal schemes in rural areas of the country.
• The scheme is being launched on a pilot basis in Maharashtra.
• It bridges the gaps for generating public awareness and reach of postal products and services, mainly in interior villages.
• Under the Five Star Village scheme, all postal products and services are going to be made available and marketed, and publicized at the village level.
• The schemes covered under the Five Star scheme include:
• ​Savings Bank accounts, Recurrent Deposit Accounts, NSC / KVP certificates.
• Sukanya Samridhi Accounts/ PPF Accounts.
• Funded Post Office Savings Account linked India Post Payments Bank Accounts.
• Postal Life Insurance Policy/Rural Postal Life Insurance Policy.
• Pradhan Mantri Suraksha Bima Yojana Account / Pradhan Mantri Jeevan Jyoti Bima Yojana Account.

The correct answer is (A) - (4), (B) - (3), (C) - (1), (D) - (2).

Key Points

 In the given table, Biosphere reserves are given.  These are biosphere reserve of states:

• Nokrek is a biosphere reserve in Meghalaya.

• The Nokrek Biosphere Reserve is located in the northeast of India on the Tura Range, which forms part of the Meghalaya Plateau.

• ​Agasthyamalai is a biosphere reserve in Kerala.

• ​The Agasthyamala Biosphere Reserve (ABR) has got its name into UNESCO’s World Network of Biosphere Reserves (BR).

• It was established in 2001 and straddles the border of Kollam and Thiruvananthapuram Districts in Kerala and Tirunelveli and Kanyakumari Districts in Tamil Nadu, South India at the southern end of the Western Ghats.

• Nandadevi is a biosphere reserve in Uttarakhand.

• Nanda Devi Biosphere Reserve, located in the Himalayan Mountains in the northern part of the country.

• It includes core areas of the Nanda Devi and Valley of Flowers National Parks, which are one World Heritage site.

• ​​​Dehang Debang is a biosphere reserve in Arunachal Pradesh.

• Dihang-Dibang or Dehang-Debang is a biosphere reserve constituted in 1998.

• It is in the Indian state of Arunachal Pradesh.

• Biosphere reserves are areas of terrestrial and coastal ecosystems promoting solutions to reconcile the conservation of biodiversity with its sustainable use.

• They are internationally recognized, nominated by national governments, and remain under the sovereign jurisdiction of the states where they are located.

• They often include one or more National Parks and/or preserves, along with buffer zones that are open to some economic uses. Protection is granted not only to the flora and fauna of the protected region, but also to the human communities who inhabit these regions, and their ways of life.

The correct answer is Three.

Key Points

• Three teachers from Uttar Pradesh were selected for the 'National Award' on teacher day.
• The three from UP are — Mohammed Ishrat Ali, head teacher in a primary school, Rajwana in Mainpuri; Snehil Pandey, head teacher in a primary school Soharamau, Nawabganj in Unnao; and Vikas Kumar, principal, SD Inter College Meerapur, in Muzaffarnagar
• Union Education Ministry inferred the National Award to Teachers as a way of recognizing their achievements in the field of education.
• The awards were conferred by President Ram Nath Kovind on the occasion of Teacher's Day on September 5, 2020.
• 47 teachers have been selected by the government for 'National Awards to Teachers 2020.

Additional Information

• Teacher’s Day is celebrated across India today to honour Dr. Sarvepalli Radhakrishnan.
• It is observed annually on September 5, as Dr. Radhakrishnan was born on September 5, 1888.
• Dr. Sarvepalli Radhakrishnan was India's first Vice President and second President.
• Teachers' Day was first celebrated in 1962, the year he became the second President of India.
• Since then, the day has been celebrated every year. Dr. Radhakrishnan highly believed that teachers should be the best minds in the country.

The correct answer is Environmental Impact Assessment Method.

• 'Leopold Matrix’ is associated with Environmental Impact Assessment Method.
• It is a procedure for the evaluation of the effect or impact of a proposed development on the environment.​

Important Points

• Environmental Impact Assessment (EIA) is a process of evaluating the likely environmental impacts of a proposed project or development, taking into account inter-related socio-economic, cultural and human-health impacts, both beneficial and adverse.
• It is statutorily backed by the Environment Protection Act, 1986 which contains various provisions on EIA methodology and process.
• UNEP defines Environmental Impact Assessment (EIA) as a tool used to identify the environmental, social and economic impacts of a project prior to decision-making.
• It aims to predict environmental impacts at an early stage in project planning and design, find ways and means to reduce adverse impacts, shape projects to suit the local environment and present the predictions and options to decision-makers.

The correct answer is Lucknow​.

Key Points

• As announced by the Ministry of Housing and Urban Affairs, Lucknow is the cleanest city in Uttar Pradesh.
• Swachh Survekshan 2020 report was released by the Union Housing and Urban Affairs Ministry.
• Swachh Survekshan 2020 covered 4,242 cities, 62 cantonment boards and 92 Ganga towns.
• This survey was carried out in 28 days.

Additional Information

Swachh Survekshan 2020

• Indore was ranked the cleanest city in the overall category this year followed by Surat and Navi Mumbai.
• Chhattisgarh is the cleanest state in the category of states with more than 100 urban local bodies.
• Ahmedabad is India’s cleanest Megacity.
• New Delhi is the cleanest capital city.
• Chhattisgarh’s Ambikapur is the cleanest smallest city.
• Cleanest Cantonment: Jalandhar Cantt, Punjab.

The correct answer is Excise tax.

Key Points

• The state gets a share of the revenue from the Excise tax.
• Excise tax is a form of indirect tax that is levied by the Central Government of India for the production, sale, or license of certain goods.
• It is also collected by state governments for alcohol and narcotics.
• GST has now subsumed a number of indirect taxes including excise tax.
• This means excise tax, does not exist in India except on a few items such as **liquor and petroleum. **​

Additional Information

The correct answer is Dominic Thiem.

Key Points

• US Open Men's single title- Dominic Thiem (from Austria).
• US Open Women's single- Naomi Osaka (from Japan).
• The 2020 US Open was the 140th edition of tennis US open and the second Grand Slam event of the year.
• It was held on outdoor hard courts at the USTA Billie Jean King National Tennis Center in Queens, New York.
• It was held without spectators due to the COVID 19 pandemic.

The correct answer is The speaker of the Lok Sabha.

Key Points

• The joint sitting of the Indian Parliament for transacting a legislative business is presided over by The speaker of the Lok sabha.
• The joint sitting is called by the President.
• In his absence of the speaker of the Lok sabha, the sitting is presided over by the Deputy Chairman of the Rajya Sabha.
• The quorum to constitute a joint sitting: 1/10th of the total number of members of the House.
• A joint sitting of both Houses of Parliament of the Indian Constitution given in Article 108.

Additional Information

Speaker of Lok Sabha

• The speaker of Lok Sabha is a member who elected from amongst the members of the house. He chairs the house and no proceedings in the house take place in his absence.
• 1st Lok Sabha Speaker – Ganesh Vasudev Mavalankar
• 17th Lok Sabha elections (2019 General Elections), Om Birla is the speaker of Lok Sabha.

The correct answer is Esipattan-Saranath.

Key Points

• The anicient name of Kannauj is Mahoday.
• Kannauj is one of the most ancient place in India having a rich archeological and cultural heritage.
• The ancient name of this place is Kanyakubja or Mahodya (as per Balmiki Ramayana, Mahabharat and Puran) later name kanyakubja was changed as Kannauj the present name of the District.
• ​The ancient name of Mandsaur is Dashpur.
• ​Mandsaur was known as Dashpur in ancient times.
• It is also said that the name originated from Mandodri, wife of Ravana. And the ancient name Dashpur was named after her husband Dashanand, the other name of Ravana.
• The ancient name of Sarnath is Isipatana.
• ​Sarnath has been variously known as Mrigadava.
• Just 10 km north-east of Varanasi, near the confluence of the Ganga and Varuna Rivers in Uttar Pradesh, was Initially known as Isipatana.
• The ancient name of Talkad is Banvasi.
• Banavasi is an ancient town in Uttara Kannada in the state of Karnataka.

The correct answer is Article 253.

• Article 253 of the Indian Constitution empowers Parliament to make laws for implementing international agreements.
• Article 253- empowers Parliament to make any law for the whole or any part of the territory of India for implementing treaties, international agreements, and conventions.
• It enables the Government of India to implement all international obligations and commitments.

Additional Information

• Article 249- empowers the parliament to legislate with respect to a matter in the State List in the national interest.
• Article 250- According to this parliament is empowered to make laws on any item that is included in the State List for the whole or part of India, while a Proclamation of emergency is in operation.
• Article 252- It is about the Power of Parliament to legislate for two or more States by consent and adoption of such legislation by any other State.

The correct answer is (A) - (3), (B) - (1), (C) - (4), (D) - (2)​.

Key Points

• Kiratarjuniyam- It is a Sanskrit epic written in the 6th century by Bharavi.
• It is his only recognized work.
• It is an epic poem with eighteen cantos in which Lord Shiva tests the power of Arjuna, one of the Pandavas in the Mahabharata.
• Dashakumar Charitam-  It is authored by renowned Sanskrit poet Dandi.
• It relates the adventures of ten princes in their pursuit of love and royal power.
• Buddha Charitam-  It is an epic poem in the Sanskrit maha kavya style on the life of Gautam Budha by Ashvagosha, composed in the early second century.
• Vikramorvashiya-  It is a five-act Sanskrit play by ancient Indian poet Kalidasa who flourished in the 4th Century CE, on the Vedic love story of king Pururavas and an Apsara, a celestial nymph named Urvashi.

The correct answer is the President of India.

Key Points

• The appointment of acting Chief Justice is to be made by the President under Article 126 of the Constitution.
• Vacancy in the office of the Chief Justice must be filled whatever the period of vacancy.
• Article 126 – Appointment of acting Chief justice.
• Justice D Y Chandrachud is the current and 50th CJI.

Additional Information

Role of Chief Justice of India

• The Chief Justice is responsible for the allocation of work to other judges.
• The Chief Justice administers the oath of office to the President In the absence of the President and the Vice-President, the Chief Justice sits as the Acting President of India
• The Chief Justice is the ex-officio Chancellor to most autonomous law schools in India.

Eligiblity

• The individual must be a citizen of India.
• The person must not exceed 65 years of age.
• In order to be eligible to be Chief Justice of India, the person must serve as a judge at High Court for at least five years or the person should be an advocate in the High court or the Supreme court for at least 10 years or a distinguished jurist.

The correct answer is Chirand​.

Key Points

• Chirand is the early farming site located on the northern bank of the river Ganga together with two other rivers Sarayu and Son.
• Chirand is an archaeological site in the Saran district of Bihar.
• It is the first known site of the Neolithic age.
• It has a large pre-historic mound (a rounded mass projecting above a surface) containing various artifacts.
• The mound is known for its continuous archaeological record from the Neolithic age (about 2500–1345 BC) to the reign of the Pala Dynasty, which ruled this place during the pre-medieval period.
• This is probably one of the youngest date of early farming known from the Gangetic basin.

Additional Information

• T. Narsipur is a place located in the Mysore district in the Indian state of Karnataka.
• This is the place in South India where Kumbhamela is held every three years.
• The word 'Narasipura' is the name of the town, which is derived from the famous Gunja Narasimhaswamy temple that is located on the right bank of the Kabini river.

The correct answer is the Constitution.

Key Points

• The term 'Office of profit' has not been directly defined by the Constitution.
• But The Constitution of India, apart from enlisting certain qualifications for Members of Parliament and Legislative Assembly, also enumerates certain disqualifications. One of these disqualifications is holding an “office of profit”.
• Under the provisions of Article 102 (1) and Article 191 (1) of the Constitution, an MP or an MLA (or an MLC) is barred from holding any office of profit under the central or state government.
• The articles clarify that “a person shall not be deemed to hold an office of profit under the government of India or the government of any state by reason only that he is a minister”.
• A person will be disqualified if he holds any office of profit under the central or state government, other than an office declared not to disqualify its holder by a law passed by Parliament or state legislature.

 Principles for including ‘office of profit’ as a criterion for disqualification are:

• Makers of the Constitution wanted that legislators should not feel obligated to the Executive in any way, which could influence them while discharging legislative functions.
• In other words, an MP or MLA should be free to carry out her duties without any kind of governmental pressure. The intent is that there should be no conflict between the duties and interests of an elected member.
• The office of profit law simply seeks to enforce a basic feature of the Constitution- the principle of separation of power between the legislature and the executive.

The correct answer is Rahil. 

• A large tank near Mahoba, temples at Ajaygarh and Mahoba and the city of Rajavsini were built by Chandella King Rahil.
• The town Rahilya which is three km southwest of Mohaba was named after Rahil.
• The Chandela or Chandel is a Rajput clan in Central India.
• An area of the Chandelas which was otherwise called Chandela Dynasty led a great part of the Bundelkhand district of central India for a long period of time between the 10th and the thirteenth century AD.
• Chandel Dynasty is known in Indian history for Maharaja Rao Vidyadhara, who spurned the assaults of Mahmud of Ghazni.

The correct answer is Election Commission.

• While deciding any question relating to the disqualification of a Member of Parliament, the President shall obtain the opinion of the Election Commission.
• Election Commission of India is a permanent Constitutional Body.
• The Constitution provides for an independent election commission to ensure free and fair election to the Parliament, the State legislature,and the offices of President and Vice-President.
• Consists of Chief Election Commissioner +2 Election Commissioners.
• The Chief Election Commissioner is appointed by the President and the other Election Commissioners are appointed by the President after consultation with the Chief Election Commissioner, Article 324 also provides for the appointment of Regional Commissioners at the time of General Elections after consultation with the Election Commission.
• Election Commissioners are appointed for a term of 6 years.
• They are not eligible for re-appointment. Also, they cannot hold any office of profit after their retirement.
• In article 324 of the Indian constitution, it envisages the Election Commission of India (ECI).

Additional Information

The correct answer is Mohsin Fanni.

• The author of the ‘Dastane Mazahib’ which discusses the Din-i-Ilahi of Akbar, was Mohsin Fanni.
• Din-i Ilahi “the religion of God,” was a system of religious beliefs introduced by the Mughal emperor Akbar in 1582 CE.
• Akbar's idea was to combine Islam and Hinduism into one faith, but also to add aspects of Christianity, Zoroastrianism, and Jainism.
• Akbar took a deep personal interest in religious matters.
• He founded an academy, the Ibadat Khana, “the House of Worship,” in 1575, where representatives of all major faiths could meet to discuss questions of theology.

​

Akbar

• Akbar was born as Abu'l-Fath Jalal ud-din Muhammad Akbar on October 15, 1542.
• Akbar succeeded his father, Humayun, in 1556 when he was 13 years old.
• Akbar was given the nickname 'the Great' because of his many accomplishments.
• Akbar started a new religion that was based on the teachings of major religions like Hinduism, Christianity, Zoroastrianism, etc.
• This religious path was later referred to as the Din-i-illahi or Divine Monotheism.
• Historian Vinset Smith called Akbar's Din-i-ilahi as a monument of his folly not of wisdom.

The correct answer is Lentil.

• Lentil is not a Kharif Crop among the given options.

Key Points

• India has many growing seasons due to the prevalence of high temperatures over a long period. The different crop seasons are:​
• Kharif Crop​
• Crops are sown at the beginning of the southwest monsoon and harvested at the end of the South-West monsoon.
• Sown in June-July when rains first begin.
• Harvested in September-October.
• Requires a lot of water and hot weather to grow.
• Important crops: Jowar, Bajra, Soybean, Rice, Maize, Cotton, Jute, Groundnut, Sugarcane.
• Rabi crop
• Crops need a relatively cool climate during the period of growth but a warm climate during the germination of their seed and maturation.
• Sown in October-November.
• Harvested in April-May.
• Important Crops: Wheat, Barley, Gram, Linseed, Mustard, Masur, Lentil and Potatoes, Tobacco.

The correct answer is Right to mortgage and gift.

• Cultivators during the Mughal period enjoyed the Right to mortgage and gift their land.
• The Mughal dynasty was founded by Babur.
• He was a Chagatai Turkic prince and was descended from the Turkic conqueror Timur (Tamerlane) on his father’s side and Genghis Khan, on his mother’s side.
• The Mughal period was between 1526-1857.
• Mughal Empire controlled almost the entire Indian subcontinent.
• It stretched from the edges of the Indus river basin, northern Afghanistan and Kashmir in the north west to the now-Assam and Bangladesh highlands in the east, and down to the uplands of Deccan plateau in the south.

The correct answer is 40% protein and 20% oil.

Key Points

• Soybean seeds contain 40% of crude protein and about 20% of fat.
• The soybean is one of the most economical and valuable agricultural commodities because of its unique chemical composition.
• Since time immemorial, Soyabean has served as meat, milk, cheese, bread as well as oil for people across the globe.
• Soyabean is India’s one of the fastest-growing crops and a significant foreign exchange earner.

The correct answer is KC Niyogi.

Key Points

• KC Niyogi was appointed the Minister of 'Ministry of Rehabilitation' set up on 6 September 1947.
• Kshitish Chandra Neogy (1888–1970), also known as KC Neogi, was an Indian politician from West Bengal.
• He was a member of the Constituent Assembly of India, a member of the first Cabinet of independent India, and the chairman of the first Finance Commission of India.
• Neogy was elected as a member of the Constituent Assembly of India and after independence became a member of the First Cabinet of Independent India under Jawaharlal Nehru as the Minister of Relief and Rehabilitation and later as Minister for Commerce.

The correct answer is 300%.

• Crop intensity is referred to as the number of crops grown in the same field in one agriculture year.
• The formula to calculate any crop intensity is:
• ​Crop intensity= Total cropped area / Total sown Area)X100
• ​In this case, the number of different crops is 3.
• So, here the rotation intensity of Maize – Mustard – Mung crop is 300%.

Explanation:

T–h diagram of Vapour Compression Refrigeration Cycle:

The above-mentioned figure is a schematic diagram of vapour compression refrigeration cycle.

• Process 1-2: Isentropic compression in Compressor.
• Process 2-3: Constant pressure heat rejection in Condensor.
• Process 3-4: Isenthalpic expansion in expander (throttling valve).
• Process 4-1: Constant pressure heat absorption in Evaporator.

∴ the given figure represents T-h as its coordinate system.

Explanation:

where m = No. of Carbon atoms, n = No. of Hydrogen atoms, p = No. of Florine atoms, q = No. of Chlorine atoms.

If the refrigerant is Inorganic Compound

R – (Molecular Weight + 700)

Ammonia NH3 whose molecular weight is 17 and the chemical formula is R – 717.

Water H20 whose molecular weight is 18 and the chemical formula is R – 718.

Carbon dioxide CO2 whose molecular weight is 44 and the chemical formula is R – 744.

Explanation:

When a pure substance is below the triple point temperature, it will undergo a phase transition directly from the solid phase to the vapor phase upon heating. This process is known as sublimation.

1. Triple Point:

The triple point is the unique combination of temperature and pressure at which all three phases (solid, liquid, and vapor) of a substance coexist in equilibrium. Below the triple point temperature, the liquid phase cannot exist.

2. Below the Triple Point Temperature:

When the temperature of a pure substance is below the triple point, the substance cannot exist in the liquid phase. As a result, heating the solid will lead directly to sublimation, bypassing the liquid phase.

Phase Transitions Below Triple Point:

When a substance is below its triple point temperature, any heating of the solid phase will cause it to sublimate:

Sublimation:

Definition: Sublimation is the direct transition from the solid phase to the vapor phase without passing through the liquid phase.

Mechanism: As the solid is heated, the molecules gain enough energy to overcome the intermolecular forces holding them in the solid state and move directly into the vapor phase.

Examples: Dry ice (solid CO₂) sublimates at temperatures and pressures below its triple point, and iodine sublimates when heated under atmospheric pressure.

Detailed Steps of Heating a Solid Below Triple Point:

1. Starting from Solid:

The substance is initially in the solid phase with temperature below the triple point, making the liquid phase unstable.

2. Heating the Solid:

As heat is applied to the solid, its temperature increases, and the kinetic energy of the molecules increases, making them vibrate more vigorously.

3. Sublimation Occurs:

Upon reaching a certain temperature (still below the triple point but sufficient for sublimation), the molecules at the surface of the solid gain enough energy to break free from the solid structure and enter the vapor phase.

Conclusion:

When a pure substance is below its triple point temperature, it will:

3) Vaporize or sublimate

This is because the conditions do not allow the existence of the liquid phase, and heating the solid will directly convert it to vapor.

Explanation:

Dry Bulb Temperature: 

• Actual temperature of gas or mixture of gases.
• On the psychrometric chart, it is represented on X-axis. Going from left to right, the temperature increases while going from right to left the temperature decreases.

Specific humidity/humidity ratio (ω):

• It is defined as the mass of water vapour per unit mass of dry air in a mixture of air and water vapour. It is represented by Y-axis as shown in the chart.

Dew point temperature: 

• The temperature at which the liquid droplets just appear when the moist air is cooled continuously. It is represented by a horizontal line in the chart.

Wet-bulb temperature: 

• The temperature obtained by an accurate thermometer having a wick moistened with distilled water, represented by a horizontal line on the psychrometric chart.

According to the figure, we can see if we keep the specific humidity/humidity ratio constant and increase or decrease the dry-bulb temperature, then its dew-point temperature remains the same.

A psychrometric chart is represented as shown in the figure.

Additional Information

Relative humidity:

It is defined as the mass of water vapour (or moisture) per unit mass of dry air in a mixture of air and water vapour.

It is represented by a curved line as shown in the figure below. While going from left to right i.e. away from the saturation line the relative humidity decreases and vice-versa.

Relative humidity along the saturation line is 100%.

Basic Processes in Conditioning of Air:

Sensible heating: Moisture content of air remains constant so the specific humidity/humidity ratio is constant, and dry bulb temperature increases as it flows over a heating coil.

Sensible cooling: Moisture content of air remains constant so specific humidity/humidity ratio is constant, but its dry bulb temperature decreases as it flows over a cooling coil.

Cooling and dehumidification: When moist air is cooled below its dew-point by bringing it in contact with a cold surface, some of the water vapour in the air condenses and leaves the air stream as a liquid, as a result, both the temperature and humidity ratio of air decreases.

Heating and Humidification: During winter it is essential to heat and humidify the room air for comfort. It is done by first sensibly heating the air and then adding water vapour to the air stream through steam nozzles, as a result, both the temperature and humidity ratio of air increases.

Cooling & humidification: Air temperature drops and its humidity increases. 

Heating and de-humidification: This process can be achieved by using a hygroscopic material, which absorbs the water vapour from the moisture. If this process is thermally isolated, then the enthalpy of air remains constant, as a result, the temperature of air increases.

Concept:

The change in internal energy is given by, $Δ U = m{c_v}Δ T$

Calculation:

Given:

V₂ = 2V; V₁ = V, and P₁ = P₂ = P

$Δ U = m\frac{R}{{\gamma - 1}}\left( {{T_2} - {T_1}} \right)$

where ${C_v} = \frac{R}{{\gamma - 1}}$ and ΔT = T₂ – T₁

$Δ U = \frac{1}{{\gamma - 1}}\left( {mR{T_2} - mR{T_1}} \right)$

As we know from the ideal gas equation PV = mRT.

$Δ U = \frac{1}{{\gamma - 1}}\left( {{P_2}{V_2} - {P_1}{V_1}} \right)$

$Δ U = \frac{P}{{\gamma - 1}}\left( {{}{2V} - {}{V}} \right)$

∴ we get, $Δ U = \frac{{PV}}{{\gamma - 1}}$.

Mistake Points

In the Isobaric process, pressure is constant throughout the process.

ΔW = P₂V₂ - P₁V₁ = mR(T₂ -T₁)

ΔQ = mC_p(T2 -T1)

ΔU = mC_v(T2 -T1)

Hence for isobaric process also, the change in internal energy is given by ΔU = mCv(T2 -T1)

Concept:

SHF (Sensible Heat Factor):

It is defined as a sensible heat load divided by total heat load.

${{S}}.{{H}}.{{F}} = \frac{{{{S}}.{{H}}}}{{{{T}}.{{H}}}}=\frac{S.H}{S.H;+;L.H}$

where T.H = S.H + L.H

S.H = Sensible heat T.H = Total heat L.H ⇒ Latent heat 

Calculation:

Given:

S.H = 30000 kJIhr L.H = 20000 kJIhr.

${{S}}.{{H}}.{{F}} =\frac{S.H}{S.H;+;L.H}$

${\rm{S}}.{\rm{H}}.{\rm{F}} = \frac{{30,000}}{{30,000 + 20,000}} = \frac{3}{5} = 0.60;$

Concept:

The heater acts as a work input to the system. 

Work done by heater = Power × time

According to First Law of Thermodynamics:

δQ = dU + δW

Calculation:

Given:

δQ = -300 kJ (Heat is lost), t = 10 min ⇒ 10 × 60 = 600 sec, mass m = 5 kg.

Work is done to the system, by heater:

Work done by heater (δW) = Power × time = 2 × 600 ⇒ 1200 kJ.

δQ = dU + δW

-300 = dU + (-1200)

dU = 900 kJ

We know that;

dU = mcΔT

900 = 5 × 4.18 × ΔT

ΔT = 43.06 ≈ 43.1°C.

Concept:

Nomenclature of refrigerants:

Saturated hydrocarbon refrigerant is given as C_mH_nF_pCl_q where 2m + 2 = n + p + q must be satisfied. Nomenclature is then written as R - (m - 1)(n + 1)p.

Unsaturated hydrocarbon refrigerant must satisfy 2m = n + p + q and nomenclature is then written as R - 1(m - 1)(n + 1)p.

Inorganic refrigerant uses nomenclature R - (700 + Molecular mass).

Calculation:

Given:

For R-134a, we have

m – 1 = 1 i.e. m = 2.

n + 1 = 3 i.e. n = 2 and p = 4.

It must satisfy this 2m + 2 = n + p + q therefore, we get q = 0.

∴ we get, C₂H₂F₄

Additional Information

C₂H₂F₄ has two structures out of which one is symmetrical and one is asymmetrical the 'a' in 134a stands for asymmetrical structure.

Concept:

${{\rm{M}}_{{\rm{mix}}}} = \frac{1}{{\frac{{{{\rm{X}}_1}}}{{{{\rm{M}}_1}}} + \frac{{{{\rm{X}}_2}}}{{{{\rm{M}}_2}}}}}$

Where

M_mix = Molecular weight of the mixture.

X₁ X₂ = Mass fraction of oxygen and nitrogen.

Mass fraction = The mass fraction is the ratio of the mass of a component in the mixture to the total mass of the mixture. 

M₁ M₂ = Molecular weight of oxygen and nitrogen.

Calculation:

Given:

Mass of oxygen and nitrogen is 4 kg and 6 kg.

∴ ${{\rm{X}}_1} = \frac{4}{{10}} = 0.4,;{{\rm{X}}_2} = \frac{6}{{10}} = 0.6;$

M₁ M₂ = 32 28.

By using the above formula

${{\rm{M}}_{{\rm{mix}}}} = \frac{1}{{\frac{{0.4}}{{32}} + \frac{{0.6}}{{28}}}} = 29.47$

Concept :

Coefficient Of Performance (COP) Or Energy Performance Ratio:

It is defined as, “The ratio of the desired effect to the work input.”

${{COP}} = \frac{{{{Desired; Effect}}}}{{{{Work;input}}}}$

Relationship between COP_HP and COP_Ref (For same temperature Limits)

COP_{Heat Pump} = 1 + COP_Ref

Calculation:

Given:

Work Input = 1 kW, COP_Ref = 4.

COP_{Heat Pump} = 1 + COP_Ref

$CO{P_{Heat\ Pump}} = \frac{{Desired;Effect;\left( {Heating;Effect} \right)}}{{Work;Input}}$

Desired effect (Heating effect) = COP_{Heat Pump} × Work Input = 5 × 1 ⇒ 5 kW.

Concept :

Available energy’ is the maximum portion of energy that could be converted into useful work by ideal processes that reduce the system to a dead state (a state in equilibrium with the earth and its atmosphere).

The fraction of available energy is lost in the process is given by

$\Delta E = \left( {\frac{{{T_0}}}{{{T_1-T_0}}}} \right)\times \left( {\frac{{{T_1-T_2}}}{{{T_2}}}} \right)$

T₁ = Condensing Temperature K, T₂  = Evaporating Temperature K, T_o = Ambient Temperature K.

Calculation:

Given:

T_o  = 273 + 35 = 308 K; T₁ = 273 + 420 = 693 K; T₂ = 273 + 250 = 523 K.

$\Delta E = \left( {\frac{{{T_0}}}{{{T_1-T_0}}}} \right)\times \left( {\frac{{{T_1-T_2}}}{{{T_2}}}} \right)$

$\Delta E = \left( {\frac{{{308}}}{{{693-308}}}} \right)\times \left( {\frac{{{693-523}}}{{{523}}}} \right)=0.26$

Explanation:

Secondary refrigerants:

Usually, liquids and air are used to transfer heat from the substance being cooled to a heat exchanger where the heat is absorbed by a primary refrigerant. In an air conditioning system, it could be said that air is acting as a secondary refrigerant.

Properties of Refrigerants:

• Low freezing point: When the refrigerant goes through the expansion valve in the refrigeration cycle, it experiences a tremendous pressure drop and hence a tremendous decrease in temperature as well. It is therefore important that the refrigerant has a low freezing point than the normal operating conditions.
• Low viscosity: For the easy flow of refrigerants.
• Good stability: It should be chemically stable for the operating ranges of temperature. Also, it should not react with the materials of the refrigeration system or with which it comes into contact.
• Low vapor pressure: Condenser pressure of the refrigerator should be moderate and the evaporator pressure of the refrigerator should be around atmospheric pressure.

Additional Information

Other Important Properties of Refrigerants:

Concept:

Change in entropy for Ideal gas is given by :

$Δ s = {c_p} \ln \left( {\frac{{{T_2}}}{{{T_1}}}} \right) - R \ln \left( {\frac{{{P_2}}}{{{P_1}}}} \right)$

$Δ s = {c_v} \ln \left( {\frac{{{T_2}}}{{{T_1}}}} \right) + R\ln \left( {\frac{{{V_2}}}{{{V_1}}}} \right)$

$Δ s = {c_p} \ln \left( {\frac{{{V_2}}}{{{V_1}}}} \right) + {c_v}\ln \left( {\frac{{{P_2}}}{{{P_1}}}} \right)$

Calculation:

Given:

Option (1)

P₁ = 6 bar, P₂ = 3 bar, T₁ = T₂, and R = 0.287 kJ/kg-K. 

$Δ s = {c_p} \ln \left( {\frac{{{T_2}}}{{{T_1}}}} \right) - R \ln \left( {\frac{{{P_2}}}{{{P_1}}}} \right)$

$Δ s = {c_p}\ln \left( {\frac{{{T_2}}}{{{T_2}}}} \right) - 0.287\ln \left( {\frac{3}{6}} \right)$

= 0.1989 kJ/kg (change in entropy is positive).

Option (2) 

P₁ = P₂;  ${V_2} = \frac{{{V_1}}}{2}$

$Δ s = {c_p} \ln \left( {\frac{{{V_2}}}{{{V_1}}}} \right) + {c_v}\ln \left( {\frac{{{P_2}}}{{{P_1}}}} \right)$

$Δ s = 1.005\ln \left( {\frac{1}{2}} \right) + {c_v}\ln \left( {\frac{{{P_1}}}{{{P_1}}}} \right)$

Δs = -0.6966 kJ/kg-K (change in entropy is negative).

Correct answer

Option (3) 

P₂ = 2P₁; V₁ = V₂

$Δ s = {c_p} \ln \left( {\frac{{{V_2}}}{{{V_1}}}} \right) + {c_v}\ln \left( {\frac{{{P_2}}}{{{P_1}}}} \right)$

$Δ s = {c_p} \ln \left( {\frac{{{V_1}}}{{{V_1}}}} \right) + {c_v} \ln \left( {\frac{2}{1}} \right)$

= 0.49698 kJ/kg-K (change in entropy is positive).

Option (4) 

for the reversible adiabatic process of an ideal gas

Δs = 0 (change in entropy is zero).

Explanation:

Human Comfort:

The physical comfort of the human being which can be adjusted by adjusting the temperature, humidity, air velocity, and purity of the air is called human comfort.

Dry Bulb Temperature:

It is the normal temperature measured by an ordinary thermometer.

Dew Point Temperature:

The temperature of the air up to which the air should be cooled so that the water vapour present in the air starts condensing when cooled at constant pressure.

Relative humidity (RH):

Relative humidity refers to the moisture content (i.e. water vapour) of the atmosphere, as a percentage of the amount of moisture that can be retained by the atmosphere (moisture-holding capacity) at a given temperature and pressure without condensation.

Effective temperature:

• It is the temperature of the saturated environment with negligible air velocity at which the person feels the same level of comfort as the normal person.
• Effective temperature for winter is 20˚C and for summer it is 21.6˚C.

Explanation:

Biot number:

It is defined as the ratio of internal conductive resistance offered by the body to the external convective resistance.

$Bi=\frac{\frac{L}{kA}}{\frac{1}{hA}}=\frac{hL}{k}$

Biot number properties:

• Biot number is used as a criterion for lumped heat analysis.
• Low biot number values signify that the body offers very little conductive resistance for any internal heat transfer within the body.
• During unsteady-state heat transfer if the biot number is less than 0.1 then the temperature is the function of time only, it is not the function of space.
• On the other hand, if the biot number is more than 0.1 then the temperature is the function of space and time.

Additional Information

Lumped heat analysis:

In this analysis it is assumed that the temperature of the body is uniform throughout its mass at any instant of time i.e., Internal temperature gradient are negligibly small at any instant of time.

i.e.,

T = f(time), T ≠ f(space)

where, T ⇒ Temperature.

Concept:

Specific humidity (ω) or Absolute humidity or humidity ratio:

Mass of water vapor in a unit mass of dry air usually expressed as grams of vapor (v) per kilogram of dry air (d.a).

\({{\omega }} = \left( {\frac{{{{\rm{m}}{\rm{v}}}}}{{{{\rm{m}}{\rm{a}}}}}} \right)\frac{{{\rm{gm}}\left( {\rm{v}} \right)}}{{{\rm{kg}}\left( {{\rm{d}}.{\rm{a}}} \right)}}\)

It is also given by:

\(\omega = 0.622 \times \left( {\frac{{{{\bf{P}}{\bf{v}}}}}{{{{\bf{P}}{\bf{t}}} - {{\bf{P}}_{\bf{v}}}}}} \right)\frac{{{\bf{gm}}\left( {\bf{v}} \right)}}{{{\bf{kg}}\left( {{\bf{d}}.{\bf{a}}} \right)}}\)

Pt = Pv + Pa

where, P_t = total pressure, P_v = partial pressure of vapour, P_a = partial pressure of air.

Calculation:

Given:

Pt = 0.1 MPa, Pv = 1.5 × 10-3 MPa.

\(\omega = 0.622 \times \left( {\frac{{{{\bf{P}}{\bf{v}}}}}{{{{\bf{P}}{\bf{t}}} - {{\bf{P}}_{\bf{v}}}}}} \right)\)

$\omega = 0.622 \times \left( {\frac{{1.5 \times {{10}^{ - 3}}}}{{0.1 - 1.5 \times {{10}^{ - 3}}}}} \right)$

ω = 9.47 gm/kg-da.

Concept:

Absorptivity (α):

Fraction of radiant energy incident upon a surface which is absorbed by it.

Reflectivity (ρ):

 Fraction of radiant energy incident upon a surface which is reflected by it.

Transmissivity (τ):

Fraction of radiant energy incident upon a surface which is transmitted through it.

For any Surface,

α + ρ + τ = 1

Calculation:

Given:

τ = 0.86, ρ = 0.08

substituting all the values in the equation we have;

α + 0.08 + 0.86 = 1

α = 1 – 0.08 – 0.86

α = 0.06

Concept:

RSHF (Room Sensible Heat Factor): It is defined as sensible heat load divided by total heat load in a room.

RTH = Room Total Heat, RSH = Room Sensible Heat, RLH = Room Latent Heat.

RTH = RSH + RLH ……….(I)

${\bf{RSHF}} = \frac{{{\bf{RSH}}}}{{{\bf{RTH}}}}$ ..... (II)

RLH = 50 × cmm × (ω₁ – ω₂) .....(III) 

where, cmm is cubic meter per minute i.e., air changes per minute.

ω₁, ω₂ = specific humidity of the room and supplied air.

Calculation:

Given:

RSHF = 0.75, RTH = 100 kW, Air changes per minute = 100 m³/min ⇒ 100 × 10⁶ cm³/min.

By using equation (II)

${{RSHF}} = \frac{{{{RSH}}}}{{{{RTH}}}}$

RSH = 0.75 × 100 kW = 75 kW.

By using equation (I)

RTH = RSH + RLH

RLH = 100 – 75 = 25 kW.     

By using equation (III)

RLH = 50 × cm; × (ω1 – ω2)

25 = 50 × 100 × (ω₁ - ω₂)

(ω1 - ω2) = 0.005

0.01 - ω2 = 0.005

ω₂ = 0.005 kg/kg of dry air**.**

Concepts:

Effectiveness of the heat exchanger: 

The effectiveness (ϵ) of a heat exchanger is defined as the ratio of the actual heat transfer to the maximum possible heat transfer.

Actual heat transfer = Q = m_hc_ph(t_h1 − t_h2) = m_cc_pc(t_c2 − t_c1) 

where m_hc_ph = C_h = hot fluid capacity rate; m_cc_pc = C_c = Cold fluid capacity rate.

Maximum possible heat transfer = C_min(t_h1 - t_c1); where C_min is minimum of (Ch, Cc)

$\varepsilon = \frac{{{C_h}\left( {{t_{h1}} - {t_{h2}}} \right)}}{{{C_{\min }}\left( {{t_{h1}} - {t_{c1}}} \right)}} = \frac{{{C_c}\left( {{t_{c2}} - {t_{c1}}} \right)}}{{{C_{\min }}\left( {{t_{h1}} - {t_{c1}}} \right)}}$

Calculation:

Given:

th1 = 76°C; th2 = 47°C; tc2 = 57°C ; tc1 = 28°C; Ch = Cc

$\varepsilon = \frac{{{C_h}\left( {{t_{h1}} - {t_{h2}}} \right)}}{{{C_{\min }}\left( {{t_{h1}} - {t_{c1}}} \right)}} = \frac{{{C_c}\left( {{t_{c2}} - {t_{c1}}} \right)}}{{{C_{\min }}\left( {{t_{h1}} - {t_{c1}}} \right)}}$

$\varepsilon = \frac{{\left( {76 - 47} \right)}}{{\left( {76 - 28} \right)}} = 0.60$

Adiabatic Cooling is a psychrometric process that involves the cooling of air without heat loss or gain. Sensible heat lost by the air is converted to latent heat in the added water vapour.

During Adiabatic cooling enthalpy remains constant and in the psychometric chart the WBT lines and the enthalpy lines have the same slope therefore the WBT will also remain constant during the adiabatic cooling process.

Explanation:

Plane wall with Internal Heat Generation

Temperature distribution of plane wall with uniform internal heat generation is given by:

$T = {T_∞ } + \frac{{{q_g}(2L)}}{{2h}} + \frac{{{q_g}}}{{8k}}\left( {{4L^2} - 4{x^2}} \right)$ (parabolic Equation)

where, slab thickness = 2L, in the region 0 < x < 2L ; k = thermal conductivity (W/mK), h = heat transfer coefficient (W/m²K), q_g = uniform heat generation (W/m³), and T∞ = ambient temperature.

At x = L; T = T_max    

$T_{max} = {T_∞ } + \frac{{{q_g}(2L)}}{{2h}}$

∴ $\frac{{\delta T}}{{\delta x}} = 0$.

At x = L, signifies the centre line of the slab.

Explanation:

V - C cycle is represented by 1-2-3-4-1

V - C cycle with superheating in the evaporator is represented by 1'-2'-3-4-1'

Following points are to be noted after the superheating in the evaporator

• Refrigeration effect → increases as $\left[ {h_1' - {h_4} > {h_1} - {h_4}} \right]$
• Wc i.e. compressor work depends on the compressor inlet temperature, as

  ${W_c} = \frac{{\gamma R{T_1}}}{{\gamma - 1}}\left[ {{{\left( {\frac{{{P_2}}}{{{P_1}}}} \right)}^{\frac{{\gamma - 1}}{\gamma }}} - 1} \right]$. So, Wc = increases

• $COP = \frac{{RE}}{{{W_c}}}$ = May increase or decrease depending upon the refrigerant used.

Concept:

Shape Factor is defined as the fraction of radiation energy leaving a surface that reaches another surface, for example, F₁₂ means the fraction of energy leaving the surface 1 reaches surface 2.

Summation Rule: F11 + F12 = 1

Reciprocity theorem: A1 F12 = A2 F21 (A is the surface area)

Calculation:

Given:

Let us denote the hemishpherical body as body 1, and the flat surafce as body 2

From the summation rule F₂₂ + F₂₁ = 1, 

Since no radiation leaving the surface 2 will reach surface 2 again 

∴ F₂₂ = 0, F₂₁ = 1

Now from reciprocity theorem,

A1 F12 = A2 F21

2 x π x r² x F12 = π x r² x1

∴ F₁₂ = 0.5,

Now from summation rule F12 + F₁₁ = 1, F₁₁ = 1 - 0.5 = 0.5

Therefore the shape factor of hemispherical body with respect to itself is 0.5.

Concept:

Air washer:

• Air washer is a device for conditioning air.
• In an air washer air comes in direct contact with a spray of water and there will be an exchange of heat and mass (water vapour) between air and water.
• The outlet condition of air depends upon the temperature of the water sprayed in the air washer.
• By controlling the water temperature externally, it is possible to control the outlet condition of air, which then can be used for conditioning purpose.

Various processes that take place in the air washer:

Let, t_w = water sprayed temperature, DPT→ Dew point temperature, DBT→ Dry bulb temperature.

• Cooling and Dehumidification, tw < DPT
• Adiabatic saturation, t_w = t_WBT
• Cooling and humidification, t_DPT < t_W < t_DBT

Calculation:

Given:

t_w = 25°C, DBT = 35°C, DPT = 20°C

In the above data  tDPT < tW < tDBT

Hence it is the case of cooling and humidification.

Explanation:

Overall heat transfer coefficient (OHTC):

• OHTC is defined as the quantity of rate of heat transfer takes place due to any mode per unit area for unit temperature difference.
• It doesn’t have any physical meaning, it’s an experimentally determined coefficient value.
• The concept of OHTC is valid for a steady-state.
• In the case of a heat exchanger, there is a combined mode of heat transfer or multiple resistances present therefore we use,

​$Q = ;UA{\bf{\Delta }}T \Rightarrow UA = \frac{1}{{{R_{Total}}}}$, 

where R Total is total resistance and U = OHTC

• Unit of ‘U’ is W/m2K
• U indicates the quantity of rate of heat transfer takes place due to any mode per unit area for the unit temperature difference.

Fouling factor indicates the resistance offered due to chemical deposits and scaling.

So, $\frac{1}{{{U_{with;fouling}}}} = \frac{1}{{{U_{without;fouling}}}} + F$

Calculation:

Given:

Uo = 400 W/m2K, $F=\frac{1}{{2000}}\frac{m^2K}{{{}W}}$

$\begin{array}{l} \therefore \frac{1}{{{U_{with;fouling}}}} = \frac{1}{{400}} + \frac{1}{{2000}}\ \Rightarrow {U_{with;fouling}} = 333\frac{W}{{{m^2}k}} \end{array}$

Explanation:

Humidity ratio/Specific humidity (ω ) (kg/kg) of a given moist air sample is defined as the ratio of the mass of water vapour (mw) to the mass of dry air (ma) contained in the sample.

$w = \frac{{{m_w}}}{{{m_a}}} = 0.622\frac{{{P_v}}}{{P - {P_v }}}$

Relative humidity (ϕ):

It is defined as the ratio of partial pressure of water vapour (pv)in a mixture to the saturation pressure (ps) of pure water at the same temperature of the mixture.

$\phi = \frac{{{p_v}}}{{{p_{vs}}}}$

Degree of saturation (μ) is the ratio of the humidity ratio (w) to the humidity ratio of a saturated mixture (ws) at the same temperature and pressure. It is also called saturation ratio or percentage humidity.

$\begin{array}{l} {\rm{w}} = \frac{{{\rm{kg;of;water;vapour}}}}{{{\rm{kg;of;dry;air}}}} = 0.622\frac{{{p_v}}}{{{p_a} - {p_v}}}\ \mu = \frac{w}{{{w_s}}} = \frac{{{P_v}}}{{{P_{vs}}}}\left( {\frac{{P - {P_{vs}}}}{{P - {P_v}}}} \right) \end{array}$

Concept:

For counterflow heat exchanger:

Log mean temperature difference is given by:

$LMTD = \frac{{{\rm{Δ }}{T_i}; - ;{\rm{Δ }}{T_e}}}{{\ln \left( {\frac{{{\rm{Δ }}Ti}}{{{\rm{Δ }}Te}}} \right)}}$

Where ΔTi = Thi – Tce

ΔTe = The - Tci

Thi & Tci = Temperature at which hot or and cold water enters respectively

The & Tce = Temperature at which hot air & cold water exits respectively

In case of the balanced counter flow heat exchanger, 

ṁ_hc_h = ṁ_cc_c = C

ṁ_h and ṁ_c are mass flow rate of hot and cold fluid, and c_h and c_c specific heat capacity of hot and cold fluid.

LMTD for counter-flow heat exchanger, ΔT_i = ΔT_e

Calculation:

Given:

Thi = 60 °C , Tce = 30 °C

ṁh = 1 kg/s and ṁc =  2 kg/s, ch = 10 kJ/kgK, cc = 5 kJ/kgK

Here, ṁhch = ṁccc = 2 × 5 = 1 × 10 = 10

Hence it is a balanced counter-flow heat exchanger

∴ LMTD = ΔTi = Thi – Tce = 60 - 30 = 30 °C

Concept:

In an Otto, cycle efficiency is given as

$η = 1 - {\left( {\frac{1}{r}} \right)^{\gamma - 1}}$

Where r is the compression ratio and γ is the ratio of specific heat

Also compression ratio

$r = \frac{{volume;before;compression}}{{volume;after;compression}} = \frac{{{V_s} + {V_c}}}{{{V_c}}}$

Vs = Stroke volume or volume of cylinder = $\frac{\pi }{4};{d^2};l$

Vc = Clearance volume

Calculation:

Given:

V_c = 10% of V_s = 0.1Vs

Compression ratio, r = V_c + V_s/V_c = 0.1V_s + V_s/0.1Vs = 11

$η = 1 - {\left( {\frac{1}{11}} \right)^{1.4 - 1}}$

η = 61.67%

Concept:

Prandtl Number: It is defined as the ratio of momentum diffusivity to thermal diffusivity.

$Pr = \frac{\nu }{\alpha } = \frac{{momentum;diffusivity}}{{Thermal;diffusivty}} = \frac{{\frac{\mu }{\rho }}}{{\frac{k}{{{c_p}\rho }}}} = \frac{{\mu {c_p}}}{k}$

The relationship between the thermal boundary layer and the hydrodynamic boundary layer is given by the Prandtl number.

${δ _t} = \frac{δ }{{{{\left( {Pr} \right)}^{\frac{1}{3}}}}}$

where δ = hydrodynamic boundary layer thickness and δ_t = thermal boundary layer thickness.

Calculation:

Given:

δ = 0.5 mm.

$Pr = \frac{{\mu {C_p}}}{k} = \frac{{25 \times {{10}^{ - 6}} \times 2 \times 10^3}}{{0.05}} = 1$

${δ _t} = \frac{δ }{{{{\left( {Pr} \right)}^{\frac{1}{3}}}}}$

δ_t = δ = 0.5 mm.

Concept:

When the spark is advanced, burning gas is compressed by the rising piston and therefore temperature and pressure are increased, thus, the tendency to knock increases.

In spark ignition (SI) engines, the possibility of knocking can be reduced by decreasing the compression ratio as a reduction in the compression ratio will result in the generation of lower peak temperatures. In SI engine, knocking occurs before TDC and because of early combustion of charge/more than one flame propagation.

Factors affecting knocking in SI engine:

Compression ratio:

• Higher compression ratio will result in the higher temperature of the charge, the tendency to knock will increase.

Inlet air temperature:

• The effect of inlet air temp is the same as compression ratio. High inlet temp of the air-fuel mixture will increase knocking.

Advancing the spark:

• Advancing the spark will result in more compression during sparking. The increase in temperature during the sparking will be higher. Hence tendency to knock will increase and so by retarding the spark, the tendency to knock will decrease.

Coolant water temperature: 

• By increasing coolant water temperature, less heat will be carried from the engine which will increase the engine temperature. So the knocking will increase.

Engine Speed:

• To avoid the knocking in the SI engine the engine speed should be high.

Octane rating:

• It should be as high as possible.

Concept:

According to Fourier’s law, the rate of heat flow, Q through a homogeneous solid is directly proportional to the area A, of the section at the right angles to the direction of the heat flow, and to the temperature gradient (dT/dx) along the path of heat flow.

$Q = - kA\frac{{dT}}{{dx}};$

$\dot Q = kA\frac{{\left( {{T_1} - {T_2}} \right)}}{L} = \frac{{{\rm{\Delta }}T}}{{{R_{cond}}}}$

Heat Transfer in the wall is given as $Q = \frac{{{\rm{\Delta }}T}}{{{R_{th}}}}$

∴ ${R_{th}} = \frac{l}{{kA}}$

Calculation:

Given:

l = 0.6 m, A = 1.5 m2 ,k = 0.4 W/mK

$\begin{array}{l} {R_{th}} = \frac{{l}}{kA}\ = \frac{{0.6}}{{0.4 \times 1.5}} = 1;K/W \end{array}$

Explanation:

• Cavitation is the phenomenon of the formation of vapour bubbles of a flowing liquid in a region where the pressure of the liquid falls below the vapour pressure and sudden collapsing of these vapour bubbles in a region of higher pressure.
• When the vapour bubbles collapse, very high pressure is created.
• The metallic surfaces, above which the liquid is flowing, is subjected to these high pressure which causes pitting action on the surface.
• Thus cavities are formed on the metallic surface and hence the name is cavitation.
• In centrifugal pumps, the cavitation may occur at the inlet of the impeller of the pump or at the suction side of the pumps, where the pressure is considerably reduced.
• Hence if the pressure at the suction side of the pump drops below the vapour pressure of the liquid then the cavitation may occur.

Concept:

Effectiveness – The effectiveness of the heat exchanger is defined as the ratio between the actual heat transfer rate taking place between hot and cold fluids and the maximum possible heat transfer rate between them.

\(\varepsilon = \frac{{{{\dot q}{act}}}}{{{{\dot q}{max}}}}\)

Effectiveness for a counter flow heat exchanger:

${\varepsilon _{counter}} = \frac{{1 - {e^{ - \left( {1 - C} \right)NTU}}}}{{1 - C{e^{ - \left( {1 - C} \right)NTU}}}}$

where C = Heat capacity ratio C_min/C_max.

Number of Transfer Unit (NTU)

$NTU = \frac{{UA}}{{{{\left( {\dot m{C_p}} \right)}_{small}}}}$

When hot and cold fluids have equal capacity rate, C = 1

${\varepsilon _{counterflow}} = \frac{{NTU}}{{1 + NTU}}$

Calculation:

Given:

NTU = 0.5, Cph = Cpc, ∴ C = 1.

${\varepsilon _{counterflow}} = \frac{{NTU}}{{1 + NTU}}$

$\varepsilon_{counter;flow} = \frac{{0.5}}{{0.5+1}} = \frac{1}{3} = 0.33$

CH₄ + 2O₂ → CO₂ + 2H₂O

2 Volume of O₂ is present in $\frac{{100 \times 2}}{{21}} = 9.352;by;volume;of;air$

**Concept:**​​​

${N_u} = \frac{{hD}}{K}$

where D is the characteristic dimension of the body.

For vertical plate case D = L

Rayleigh Number (Ra) = Gr.Pr

$= \frac{{g\beta {\rm{\Delta }}T{L^3}}}{{{v^2}}} × Pr$

Nu = K(Ra)1/4

​$Nu = K{\left[ {\frac{{g\beta {\rm{\Delta }}T{L^3}}}{{{v^2}}} × Pr} \right]^{1/4}}$​