Question

Density $\left(\rho \right)$ versus internal energy ($U$) graph of a gas is as shown in figure. Choose the correct options

• A. $Q_{bc}=0$
• B. $W_{bc}=0$
• C. $W_{ca}<0$
• D. $Q_{ab}>0$

Answer 1

Answer: (C), (D)

The correct options are
C $W_{ca}<0$
D $Q_{ab}>0$

$\rho$ is representation of $\frac{1}{V}$ and $U$ is representation of $T$. In path bc, $\frac{\rho }{U}=constant$, hence $VT=constant$ which does does not has $W=0$. Also, since $V$ is not constant, W is non zero.

In path ca, $\rho$ increases and hence $V$ decreases, therefore, $W_{ca}<0$.

In path ab, $V$ is constant, hence $W_{ab}=0$ but $\Delta U>0$ and hence $Q_{ab}>0$.