A tank of volume$0.2{\text{m}}^{\text{3}}$ contains helium gas at a temperature of 300 K and pressure $1.0\times {10}^5{\text{Nm}}^{-2}$ . If the molar specific heat capacity of helium at constant volume is$3.0\text{cal/mol}-\text{K}$ , then the amount of heat required to raise the temperature to 400 K is

${\text{t}}_{\text{1}}=300\text{k}$

$\text{P}=\text{1}{\text{.0×10}}^5{\text{Nm}}^{-2}$

${\text{C}}_{\text{v}}=3{\text{calmol}}^{-1}{\text{k}}^{-1}$

$\left(\begin{array}{c}\text{we}\text{know}\text{PV}=\text{nRT}\\ \text{ n}=\frac{\text{PV}}{\text{RT}}\end{array}\right)$

$\text{t}=400\text{k}$

$\text{Q}=\text{?}$

$\Delta \text{t}=400\text{K}-300\text{K}$ $=100\text{K}$

$\text{Q}={\text{C}}_{\text{v}}\text{n}\Delta \text{t}=3\times 4.18\times \frac{\text{PV}}{\text{RT}}\times 100$

$=\frac{3\times 4.18\times 1\times {10}^5\times 0.2\times 100}{8.3\times 300}$

$=\frac{0.836\times {10}^5}{8.3}=\frac{836}{83}\times {10}^3$

$=10.55\times {10}^3$

$\Rightarrow \text{Q}=10550\text{J}=2511\text{cal}$