Question

When a gas filled in a closed vessel is heated through $1^{0}C$, its pressure is increased by 0.4%. The initial temperature of the gas was:

• A. $250K$
• B. $2500K$
• C. ${250}^{0}C$
• D. ${25}^{0}C$

Answer 1

The correct option is B $2500K$

By ideal gas equation, $PV=nRT\Rightarrow \frac{P}{T}=\frac{nR}{V}=constant$ (if V is constant)

Now, let initial pressure=$P_{\circ }$, final pressure=$P_{\circ }+0.04$

let final temp. = T K, final temp.=T+273 K

$\therefore \frac{P_{\circ }}{T}=\frac{P_{\circ }+0.04}{T+273}\Rightarrow 1+\frac{273}{T}=1+\frac{0.04}{P_{\circ }}\Rightarrow \frac{273}{T}=\frac{0.04}{P_{\circ }}\Rightarrow T=\frac{273}{0.04}{P}_{\circ }=2500K$