Question

The temperature of $n$ moles of an ideal gas is increased from $T$ to $4T$ through a process for which pressure $P=a{T}^{-1}$ , where $a$ is a constant. The work done by the gas is

• A. $nRT$
• B. $4nRT$
• C. $2nRT$
• D. $6nRT$

Answer 1

Answer: (D)

According to ideal gas equation
$PV=nRT$
$\text{or}V=\frac{nRT}{P}$
$\because P=\frac{a}{T}\left(\text{Given}\right)\dots \left(\text{i}\right)$
$\because V=\frac{nRT{}^2}{a}$
$\Rightarrow \text{dV}=\frac{2nRT}{\text{a}}\text{dT}$
Work done by the gas, $\text{dW = PdV}$
$\text{or }\text{W}=\underset{T}{\overset{4T}{\int }}\frac{a}{T}\frac{2nRT}{a}dT\dots \left(\text{Using (i) and (ii)}\right)$
$={\left[2nRT\right]}_T^{4T}=6nRT$