Question

Two moles of an ideal monoatomic gas undergoes a cyclic process $ABCA$ as shown in the $V-T$ diagram above.
Then, which of the following statements is/are correct? [$R$ is a gas constant]

• A. Work done on the gas during the $BC$ process is $600R$
• B. Heat supplied to the gas during the $BC$ process is $1500R$
• C. Heat supplied to the gas during the $AB$ process is $600Rln2$
• D. Work done by the gas during the entire cycle is $600R(ln2-1)$

Answer 1

Answer: (A), (C), (D)

The correct options are
A Work done on the gas during the $BC$ process is $600R$
C Work done by the gas during the entire cycle is $600R(ln2-1)$
D Heat supplied to the gas during the $AB$ process is $600Rln2$

(A) During the process $BC$, $VT$ is constant. It is a polytropic process. Hence, $K=2$.

The work done is $W=\frac{nR}{K-1}(T_f-T_i)=\frac{2\times R}{2-1}(600-300)=600R$

Hence, work done on the gas during the $BC$ process is $600R$.

(B) The heat supplied is $q=nC(T_f-T_i)$. Here, $C=C_V+\frac{R}{1-K}=\frac{3R}{2}+\frac{R}{1-2}=\frac{R}{2}$

$q=2\times \frac{R}{2}(600-300)=300R$

Hence, the heat supplied to the gas during the $BC$ process is $300R$.

(C) The process $AB$ is the isothermal process. The heat supplied is

$q=-W=nRTln\frac{V_f}{V_i}=2\times R\times 300ln\frac{4}{2}=600Rln2$

Hence, the heat supplied to the gas during the $AB$ process is $600Rln2$.

(D) The work done by the gas during the entire cycle is

$W_{AB}+W_{BC}+W_{CA}=600Rln2-600R+0=600R(ln2-1)$

Hence, the work done by the gas during the entire cycle is $600R(ln2-1)$.