Question

An ideal system operating with n moles of an ideal monatomic gas performs the cycle shown in the $P-V$ diagram to the right. All parts of the cycle are carried out slowly and reversibly. Starting at state a, where its volume and pressure are $(V_0,p_0)$, the gas undergoes an isothermal expansion until it reaches state b where its volume and pressure are $(8V_0,p_0/8)$. In process $b\to c$ the gas is cooled at constant volume to $(8V_0,p_0/32)$. Process $c\to a$ is an adiabatic compression back to state a.

Select incorrect statement:

• A. $a\to b$, there is no change in internal energy of gas
• B. $c\to a$, there is no change in entropy of gas
• C. $b\to c$, there is no work done by gas
• D. $a\to b\to c\to a$, there is work done by gas in cyclic process

Answer 1

Answer: (B), (D)

The correct options are
B $c\to a$, there is no change in entropy of gas
D $a\to b\to c\to a$, there is work done by gas in cyclic process

In the $P$ vs $V$ diagram the work done is area under the curve.

1. The work done for the path $a$ to $b$ is positive (let say $W1$). (volume is increasing) . the isothermal process, i.e. internal energy is not equal to 0.
2. The work done for path $b$ to $c$ is 0. (no change in volume).
   
3. The work done for path $c$ to $a$ is negative.(say $-W2$) (volume decreasing). entropy change is negative.

Total work done $W1+0-W2$

Area under the curve ab > area under the curve $c$ to $a$

Work done $=W1-W2$ positive value.