Question

The amount of heat needed to raise the temperature of $4$ moles of a rigid diatomic gas from $0^{\circ }\text{C}$ to ${50}^{\circ }\text{C}$, when no work is done, is -

$R$ is the universal gas constant.

• A. $500R$
• B. $750R$
• C. $250R$
• D. $175R$

Answer 1

The correct option is A $500R$

From first law of thermodynamics,

$\Delta Q=\Delta U+\Delta W$

Here, $\Delta W=0$

$\therefore \Delta Q=\Delta U=n{C}_v\Delta T=\frac{nR\Delta T}{\gamma -1}$

For a diatomic gas, $\gamma =1.4$,

$\Rightarrow \Delta Q=\frac{4\times R\times 50}{1.40-1}=500R$

Hence, option $\left(D\right)$ is the correct answer.