Question

A gas cylinder has walls that can bear a maximum pressure of 1.0 × 10⁶ Pa. It contains a gas at 8.0 × 10⁵ 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:-
Maximum pressure that the cylinder can bear, P_max = 1.0 × 10⁶ Pa
Pressure in the gas cylinder, P₁ = 8.0 × 10⁵ Pa
Temperature in the cylinder, T₁ = 300 K

Let T₂ be the temperature at which the cylinder will break.
Volume is constant. Thus,         ............(Given)
V₁= V₂ = V

Applying the five variable gas equation, we get

\[\frac{P_1 V}{T_1} = \frac{P_2 V}{T_2} .........( \because  V_1  =  V_2 )\] 

\[ \Rightarrow \frac{P_1}{T_1} = \frac{P_2}{T_2}\] 

\[ \Rightarrow    T_2  = \frac{P_2 \times T_1}{P_1}\] 

\[ \Rightarrow  T_2  = \frac{1 . 0 \times {10}^6 \times 300}{8 . 0 \times {10}^5}=375K\]