Question

A gas cylinder has walls that can bear a maximum pressure of $1.0\times {10}^6$ Pa. It contains a gas at $8.0\times {10}^5$ Pa and 300 K. The cylinder is steadily heated. Neglecting any change in the volume, calculate the temperature at which the cylinder will break.

Answer 1

Given

$P_{\text{max}}=1.0\times {10}^6$ Pa,

$P_0=8.0\times {10}^5$ Pa,

$T_0$ = 300 K

Volume is constant (Given)
So Gas law,

$\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}$ $(\because V_1=V_2)$

$\frac{P_1}{T_1}=\frac{P_2}{T_2}$

or $T_2=\frac{P_{\text{max}}\times T_0}{P_0}$

= $\frac{10\times {10}^6\times 300}{8.0\times {10}^5}$

= 375 K