Question

One mole of a monatomic ideal gas goes through a thermodynamic cycle, as shown in the volume versus temperature ($V-T$) diagram. The correct statement(s) is/are:
[ $R$ is the gas constant]

• A. Work done in this thermodynamic cycle $\left(1\to 2\to 3\to 4\to 1\right)$is$\left|W\right|=\frac{1}{2}R{T}_0$
• B. The above thermodynamic cycle exhibits only isochoric and adiabatic processes
• C. The ratio of heat transfer during processes $1\to 2$ and $2\to 3is\left|\frac{Q_1\to 2}{Q_2\to 3}\right|=\frac{5}{3}$
• D. The ratio of heat transfer during processes $1\to 2$ and $3\to 4is\left|\frac{Q_1\to 2}{Q_3\to 4}\right|=\frac{1}{2}$

Answer 1

Answer: (A), (C)

$\left|\Delta Q_{\left(1\to 2\right)}\right|=n{C}_{P}dT=n\times \frac{5}{2}R\times T_0=\frac{5R{T}_0}{2}$
$\left|\Delta Q_{3\to 4}\right|=n{C}_{P}dT=n\times \frac{5}{2}R\frac{T_0}{2}=\frac{5R{T}_0}{4}$
$\left|\frac{\Delta Q_{1\to 2}}{\Delta Q_{3\to 4}}\right|=2Also\left|\Delta Q_{2\to 3}\right|=\frac{3}{2}R{T}_0$
$\frac{\left(\Delta Q_{1\to 2}\right)}{\left(\Delta Q_{2\to 3}\right)}=\frac{5R{T}_0\times 2}{2\times 3R{T}_0}=\frac{5}{3}$
$w=\sum \Delta Q$
$=\frac{R{T}_0}{2}$