Thank you for reporting, we will resolve it shortly
Q.
What is the change in internal energy of one mole of a gas, when volume changes from $V$ to $2V$ at constant pressure $P$?
Thermodynamics
Solution:
According to ideal gas equation, $PV = nRT$ When pressure is constant, $PdV = nRdT$
$P(2V - V) = nRdT$
$PV = nRdT\,...(i)$
As $\gamma=\frac{C_{P}}{C_{V}}$
$\therefore \gamma-1=\frac{C_{P}-C_{V}}{C_{V}}$
or $C_{V}=\frac{C_{P}-C_{V}}{\gamma-1}=\frac{R}{\gamma-1}\,\left(\because C_{P}-C_{V}=R\right)$
$\Delta u=\frac{PV}{\gamma-1}$ (Using (i))