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 statement(s) is/are correct?

[$R$ is 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 $600R(1-ln2)$

Answer 1

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

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

(A) Work done on the gas during the $BC$ process is $w=P\Delta V=nR\Delta T=2\times R\times (600-300)=600R$
Thus, the option $A$ is correct.

(C) The process $AB$ is isothermal.
Heat supplied to the gas during the $AB$ process is $q=-w=nRTln\frac{V_2}{V_1}=2\times R\times 300ln\frac{4}{2}=600Rln2$.
Hence, the option $C$ is correct.

(D) The work done during the process $AC$ is 0 since the volume remains constant.
Work done by the gas during the entire cycle is $w=600R-600Rln2=600R(1-ln2)$.
Thus, the option $D$ is correct.