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Which expression correctly represents the net free energy change for the formation of a spherical solid nucleus of radius R during nucleation from a melt according to the free energy concept?

In direct extrusion, the extrusion pressure p depends on the yield strength of the billet material Y, the billet diameter Db, and the extruded product diameter De. Which of the following expressions correctly gives the extrusion pressure p?

Identify the option listing exclusively defects originating from the metal rolling operation.

Which of the following combinations of statements about hot extrusion processes is completely correct?

Statements:

1. In forward hot extrusion, metal flows in the same direction as the ram movement and friction exists between the billet and the container wall.

2. In backward hot extrusion, metal flows opposite to the ram movement and billet-container friction is essentially eliminated because the billet remains stationary relative to the container.

3. In backward hot extrusion, extrusion pressure increases with billet length due to increased friction at the container wall.

4. In hot extrusion of steels, molten glass is used as a lubricant and as a thermal insulator at high temperatures.

A gas mass undergoes quasi-static compression from 100 kPa, 0.12 \( m^3 \) to 500 kPa, 0.04 \( m^3 \). Assuming that the pressure and volume are related by \( PV^n = C \).

Calculate the work done by the gas (in kJ).

2 moles of ideal gas (\( \gamma \) =1.33) undergo adiabatic compression, with temperature rising from \( 300^\circ C \) to \( 420^\circ C \).

Calculate the change in internal energy (kJ).

A heat engine drives a heat pump. The engine's rejected heat plus the pump's delivered heat both warm circulating water in building radiators. Engine efficiency is 30%; heat pump COP is 3.5.

Find the ratio of total heat to water divided by heat input to the engine.

A heat engine absorbs 1000 kW at a constant 285°C and rejects 492 kW of heat at 5°C.

Consider the following thermodynamic cycles in this regard:

1. Carnot cycle

2. Reversible cycle

3. Irreversible cycle

Which could this engine represent?

A wet steam mixture has a specific liquid volume of : \( V_f = 0.0012 m^3/kg \) and vapour specific volume, \( V_g = 1.25 m^3/kg \).

With a dryness fraction of x = 0.08, calculate the vapour's volume fraction in the mixture.

A rigid steel tank contains a liquid-vapour mixture of ammonia at 25°C. The total volume of the tank is \( 0.012 m^3 \). The critical specific volume of ammonia is: \( V_c = 0.0043 m^3/kg \).

The tank is heated slowly at constant volume.

Case 1: Total mass = 4 kg

Case 2: Total mass = 0.8 kg

What will happen to the liquid level inside the tank during heating?