Question

$70$ calories of heat are required to raise the temperature of $2$ moles of an ideal diatomic gas at constant pressure from ${30}^{\circ }C$ to ${35}^{\circ }C$. The amount of heat required (in calorie) to raise the temperature of the same gas through the same range $({30}^{\circ }C$ to ${35}^{\circ })C$ at constant volume is

• A. $30$
• B. $50$
• C. $70$
• D. $90$

Answer 1

The correct option is B $50$

$Q_1=n{C}_p△T$
$Q_2=n{C}_v△T$
$\frac{Q_2}{Q_1}=\frac{C_v}{C_p}=\frac{1}{\gamma }$
$Q_2=\frac{Q_1}{\gamma }=\frac{70}{1.4}=50cal$.