Six moles of $O_2$ gas is heated from $20$ °C to $35$ °C at constant volume. If specific heat capacity at constant pressure is 8 cal/mol-K and $R=8.31$ J/mol-K, what is change in internal energy of gas?

Given,

$n=6moles, \Delta T=35-20={15}^{\circ }C=15K,\text{Cp }=\text{ 8cal}/\text{mol}–\text{K= 8}\times \text{4}.\text{2 J}/\text{mol}–\text{K }=\text{33}.\text{6J}/\text{mol}.\text{K}$

$R=8.31J/mol-K,$ Mayor's relation can be written as, 

$\because \text{Cp}–\text{Cv}=\text{R},\text{Cv }=\text{ Cp}–\text{R}=\text{33}.\text{6}–\text{8}.\text{3}=\text{25}.\text{29J}/\text{mol}.\text{K },$

$\Delta \text{U }=\text{ n Cv}\Delta \text{T },\Delta \text{U }=\text{ 6}\times \text{25}.\text{29}\times \text{15 },\Delta \text{U}=\text{2276}.\text{1J },\Delta \text{U}=\text{541}.\text{93cal = 54}0\text{cal}$