Question

One mole of diatomic ideal gas undergoes a cyclic process ABC as shown in figure. The process BC is adiabatic. The temperatures at A, B and C are $400K,800Kand600K$ respectively. Choose the correct statement:

• A. The change in internal energy in the process AB is $-350R$.
• B. The change in internal energy in the process BC is $-500R$.
• C. The change in internal energy in whole cyclin process is $250R$.
• D. The change in internal energy in the process CA is $700R$.

Answer 1

The correct option is B The change in internal energy in the process BC is $-500R$.

For a diatomic gas,
$C_v=\frac{5}{2}R$
$\Delta U_{BA}=n{C}_V(T_B-T_A)=1\times \frac{5R}{2}(800-400)=1000R$
$\Delta U_{AC}=\Delta Q_{AC}-W_{AC}=n{C}_P(T_A-T_C)-nR(T_A-T_C)=n{C}_V(T_A-T_C)=1\times \frac{5R}{2}(400-600)=-500R$

Thus, adding up the change in internal energy in both these processes, we get change in internal energy from C to B as $500R$.
As the change in internal energy is a point function we get $U_{BC}=-500R$