Question

'$n$' moles of an ideal gas undergoes a process A$\to$B as shown in the figure. The maximum temperature of the gas during the process will be

• A. $\frac{9P_0{V}_0}{4nR}$
• B. $\frac{3P_0{V}_0}{2nR}$
• C. $\frac{9P_0{V}_0}{2nR}$
• D. $\frac{9P_0{V}_0}{nR}$

Answer 1

The correct option is A $\frac{9P_0{V}_0}{4nR}$

We need to write the relation between $P$ and $V$ and maximize the product $PV$.

$P=-\frac{P_0}{V_0}V+3P_0$-------(1)

$PV=(-\frac{P_0}{V_0}V+3P_0)V$

$nRT=PV=-\frac{P_0}{V_0}{V}^2+3P_0{V}^{}$

Differentiating w.r.t $V$ and equating to 0, we get

$V=\frac{3V_0}{2}$

from equation(i) $P=\frac{3P_0}{2}$

Hence, $T=\frac{9P_0{V}_0}{4nR}$