Question

If the volume of the given mass of a gas is increased four times, the temperature is raised from ${27}^{o}C$ to ${127}^{o}C$. The elasticity will become

• A. 4 times
• B. $\frac{1}{4}$ times
• C. 3 times
• D. $\frac{1}{3}$ times

Answer 1

The correct option is D

$\frac{1}{3}$ times

From the ideal gas equation $\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}$
$\frac{E_2}{E_1}=\frac{P_2}{P_1}=\frac{V_1}{V_2}\times \frac{T_2}{T_1}=\left(\frac{1}{4}\right)\times \left(\frac{400}{300}\right)=\frac{1}{3}\Rightarrow E_2=\frac{E_1}{3}$
i.e. elasticity will become $\frac{1}{3}$ times.