Question

If the pressure of the gas contained in a closed vessel is increased by $30\%$ when heated by $273{}^{\circ }\text{C}$ then, calculate initial temperature?

• A. $1052{}^{\circ }\text{C}$
• B. $1029\text{K}$
• C. $910{}^{\circ }\text{C}$
• D. $910\text{K}$

Answer 1

The correct option is D $910\text{K}$

Given information:
Initial pressure of the gas $P_1=P\text{atm}$
Initial temperature of the gas $T_1=T\text{K}$
Final temperature of the gas $T_2=(T+273)\text{K}$
Final Pressure of the gas $P_2=P+0.3P\text{atm}$
From Gay Lussac's law, $\frac{P_1}{T_1}=\frac{P_2}{T_2}$ at constant volume.

$\Rightarrow \frac{P}{T}=\frac{1.3P}{T+273}$

$\Rightarrow 1.3T=T+273\Rightarrow 0.3T=273$

$\Rightarrow T=910\text{K}$