Question

When the pressure of the gas contained in a closed vessel is increased by 2.5%, the temperature of the gas increases by 4 K . The initial temperature of the gas is

• A. 80 K
• B. 150 K
• C. 160 K
• D. 320 K

Hint:

$P \propto T \implies \frac{\Delta P}{P} = \frac{\Delta T}{T}$ for small changes.

Answer 1

The Correct Option is C

Step 1: Constant Volume Law
In a closed vessel, $V$ is constant, so $P \propto T \implies \frac{P_1}{T_1} = \frac{P_2}{T_2}$.
Step 2: Substitution
$P_2 = P_1 + 0.025P_1 = 1.025P_1$.
$T_2 = T_1 + 4$.
$\frac{P_1}{T_1} = \frac{1.025P_1}{T_1 + 4}$.
Step 3: Solve for $T_1$
$T_1 + 4 = 1.025T_1 \implies 0.025T_1 = 4$.
$T_1 = \frac{4}{0.025} = \frac{4000}{25} = 160 \text{ K}$.
Final Answer: (C)