Question

If pressure of a gas contained in a closed vessel is increased by 0.4% when heated by $1^{0}C$, the initial temperature must be

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

Answer 1

The correct option is A 250K

We know that $\frac{P_1}{T_1}$ = constant for constant volume.

Let the initial pressure be $P_1$ and initial temperature be $T_1$.

Thus final pressure $P_2=1.004P_1$ and final temperature $T_2=T_1+1$.

Using $\frac{P_1}{T_1}=\frac{P_2}{T_2}$
So, $\frac{P_1}{T_1}$ = $\frac{1.004P_1}{T_1+1}$

Or $T_1+1=1.004T_1$

Or $0.004T_1=1$

$\Rightarrow T_1=250K$