Question

A gas cylinder containing cooking gas can withstand a pressure 14.9 atmosphere. The pressure guage of the cylinder indicates 12 atmosphere at ${27}^{\circ }\text{C}$. Due to a sudden fire in the building, the temperature starts rising. Find the temperature ( K) when the cylinder explodes?

Answer 1

The cylinder can withstand a maximum pressure of 14.9 atm. So at this pressure, the cylinder explodes and this can be taken as the final pressure.
Given information:
Initial pressure of the gas $P_1=12$ atm
Initial temperature of the gas $T_1=(27+273)=300K$
Final pressure of the gas $P_2=14.9atm$
Final temperature of the gas $T_2=?$
From Gay lussac's law, $\frac{P_1}{T_1}=\frac{P_2}{T_2}$ at constant volume.

$\Rightarrow T_2=P_2{T}_1/P_1=\frac{14.9\times 300}{12}=372.5K$