Question

A gas cylinder containing cooking gas can withstand a pressure $15$ 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 (in Kelvin) when the cylinder explodes?

• A. $375\text{K}$
• B. $240\text{K}$
• C. $100\text{K}$
• D. $450\text{K}$

Answer 1

The correct option is A $375\text{K}$

The cylinder can withstand a maximum pressure of $15\text{atm}$. So at this pressure, the cylinder explodes and this can be taken as the final pressure.
Given information:
$\text{Initial pressure of the gas}\left(P_1\right)=12\text{atm}$
$\text{Initial temperature of the gas}\left(T_1\right)=(27+273)=300\text{K}$
$\text{Final pressure of the gas}\left(P_2\right)=15\text{atm}$
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.

$\Rightarrow T_2=P_2{T}_1/P_1=\frac{15\times 300}{12}=375\text{K}$