Question

N moles of this gas undergoes the following cyclical process composed of four reversible steps:

i. Isovolumetric cooling from state 1 (T1 and P1) to State 2 (T2 and P2);

ii. Isothermal expansion from state 2 (T2 and P2) to state 3 (T2 and P3);

iii. Isovolumetric heating from state 3 (T2 and P3) back to state 4 (T4 and P4); and

iv. Adiabatic compression from state 4 (T4 and P4) to state 1 (T1 and P1).

We know that the gas has heat capacities of CP and CV which do not change during the entire process and the rate of change of internal energy with volume is zero for this gas.

Calculate change in internal energy, change in enthalpy, entropy change, heat and work for path ii & iii. Your answers should ONLY include the terms N,R, CP, CV, b, T1, P1, P2, P3 and P4.

Answer 1

(i) Isovolumetric cooling from state 1 (T1 and P1) to State 2 (T2 and P2);

Volume will be constant

So internal energy change = nCv (T2-T1)

Heat change = nCv (T2-T1)

Work done = 0

(ii) Isothermal expansion from state 2 (T2 and P2) to state 3 (T2 and P3);

The temperatrue is constant

Change in internal energy = 0

Work done = -Heat change

Work done = nRT2 (P2/P3)

(iii) Isovolumetric heating from state 3 (T2 and P3) back to state 4 (T4 and P4);

Change in volume = 0

So work done = 0

Heat change = Internal energy change = nCv(T4-T3 )

(iv) Adiabatic compression from state 4 (T4 and P4) to state 1 (T1 and P1)

Internal energy change = nCv (T1-T4)

Change in heat = 0

Work done = nCv (T1-T4)