If the co-efficient of performance of a refrigerator is 5 and operates at the room temperature (27 °C), find the temperature inside the refrigerator.

Consider a cycle tyre being filled with air by a pump. Let V be the volume of the tyre (fixed) and at each stroke of the pump ∆V (V) of air is transferred to the tube adiabatically. What is the work done when the pressure in the tube is increased from P₁ to P₂?

In a refrigerator one removes heat from a lower temperature and deposits to the surroundings at a higher temperature. In this process, mechanical work has to be done, which is provided by an electric motor. If the motor is of 1kW power, and heat is transferred from –3°C to 27°C, find the heat taken out of the refrigerator per second assuming its efficiency is 50% of a perfect engine.

The initial state of a certain gas is (P_i, V_i ,T_i ). It undergoes expansion till its volume becomes V_f. Consider the following two cases:

(a) the expansion takes place at constant temperature.

(b) the expansion takes place at constant pressure. Plot the P-V diagram for each case. In which of the two cases, is the work done by the gas more?

Consider a P-V diagram in which the path followed by one mole of perfect gas in a cylindrical container is shown in Fig. 12.9.

(a) Find the work done when the gas is taken from state 1 to state 2.

(b) What is the ratio of temperature T₁/T₂, if V₂ = 2V₁?

(c) Given the internal energy for one mole of gas at temperature T is (3/2) RT, find the heat supplied to the gas when it is taken from state 1 to 2, with V₂ = 2V₁.