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Q. One mole of an ideal gas requires $207J$ heat to raise the temperature by $10K$ when heated at constant pressure. If the same gas is heated at constant volume to raise the temperature by the same $10K,$ the heat required is:-
(Given gas constant $R=8.3Jmol^{- 1}K$ )

NTA AbhyasNTA Abhyas 2020

Solution:

$\left(\Delta Q\right)_{P}=\mu C_{p}\Delta T\Rightarrow 207=1\times C_{p}\times 10$
$\Rightarrow C_{P}=20.7\frac{\text{ Joule }}{mol - K}.$ Also $C_{P}-C_{V}=R$
$\Rightarrow C_{V}=C_{P}-R=20.7-8.3=12.4\frac{\text{ Joule }}{mole - K}$
So, $\left(\Delta Q\right)_{V}=\mu C_{V}\Delta T=1\times 12.4\times 10=124J$