Question

One mole of an ideal mono atomic gas at temperature $T_{0}$ expands slowly according to the law $\frac{P}{V}=\text{constant.}$ If the final temperature is $2T_{0}$ , heat supplied to the gas is_​

• A. $2RT_{0}$
• B. $RT_{0}$
• C. $\frac{3}{2}\textit{RT}_{0}$
• D. $\frac{1}{2}\textit{RT}_{0}$

Answer 1

Answer: (A)

In a process PV^x = constant, molar heat capacity is given by
$C=\frac{R}{\gamma - 1}+\frac{R}{1 - x}$
As the process is $\frac{P}{V}=\text{constant.}$
i.e PV^-1 = constant, therefor, x = -1
For ideal monoatomic gas, γ = 5/3
$\therefore C=\frac{R}{\frac{5}{3} - 1}+\frac{R}{1 - \left(-1\right)}=\frac{3 R}{2}+\frac{R}{2}=\text{2}\textit{R}$
$\Delta Q=nC\left(\Delta T\right)=1\left(2 R\right)\left(2 T_{0} - T_{0}\right)=2RT_{0}$