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~

• A. 350 K
• B. 325 K
• C. 375 K
• D. 365 K

Answer 1

The correct option is C

375 K

Since for a fixed mass of gas at constant volume, P increases linearly with temperature T, and vice versa, the ratio $\left(\frac{T}{P}\right)$ will be a constant.

Initial pressure, $P_1=8.0\times {10}^{5}Pa,$

Initial temperature, $T_1=300K$,

Breaking pressure, $P_2=100\times {10}^{5}Pa$

Let the temperature at which the type reaches the breaking pressure, be $T_2$. We can write -

$\left(\frac{T_2}{P_2}\right)=\left(\frac{T_1}{P_1}\right)$

$\Rightarrow T_2=\left[\frac{P_2\times T_1}{P_1}\right]=\left[\frac{10\times {10}^5\times 300}{8\times {10}^5}\right]K$

$\Rightarrow T_2=375K$.