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Q.
One mole of an ideal monoatomic gas at temperature $T_0$ expands slowly according to the law $\frac{P}{V}.$ If the final temperature is $2T_0$ heat supplied the gas is
Thermodynamics
Solution:
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 $\frac{P}{V}=$ constant,
i.e., $PV^{-1} =$ constant, therefore, $x =-1.$
For an ideal monoatomic gas, $\gamma=\frac{5}{3}$
$\therefore C=\frac{R}{\frac{5}{3}-1}+\frac{R}{1-\left(-1\right)}=\frac{3}{2}R+\frac{R}{2}=2\,R$
$ΔQ = nC\left(ΔT\right) = 1\left(2R\right)\left(2T_{0} - T_{0}\right) = 2RT_{0}$