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 $\left(1\to2\to3\to4\to1\right)$is$\left|W\right|=\frac{1}{2}RT_{0}$
• B. The above thermodynamic cycle exhibits only isochoric and adiabatic processes
• C. The ratio of heat transfer during processes $1\to2$ and $2\to3is \left|\frac{Q_{1}\rightarrow2}{Q_{2}\to3}\right|=\frac{5}{3}$
• D. The ratio of heat transfer during processes $1\to2$ and $3\to4is \left|\frac{Q_{1}\rightarrow2}{Q_{3}\to4}\right|=\frac{1}{2}$

Answer 1

Answer: (A), (C)

$\left|\Delta Q_{\left(1\rightarrow2\right)}\right|=nC_{P}dT=n\times\frac{5}{2}R\times T_{0}=\frac{5RT_{0}}{2}$
$\left|\Delta Q_{3\rightarrow4}\right|=nC_{P}dT=n\times\frac{5}{2}R \frac{T_{0}}{2}=\frac{5RT_{0}}{4}$
$\left|\frac{\Delta Q_{1\to2}}{\Delta Q_{3\rightarrow4}}\right|=2 Also\left|\Delta Q_{2\to3}\right|=\frac{3}{2}RT_{0}$
$\frac{\left(\Delta Q_{1\to2}\right)}{\left(\Delta Q_{2\rightarrow3}\right)}=\frac{5RT_{0}\times2}{2\times3RT_{0}}=\frac{5}{3}$
$w=\sum\Delta Q$
$=\frac{RT_{0}}{2}$