Question

If pressure of a gas contained in a closed vessel is increased by 0.4% when heated by 1⁰C, the initial temperature must be

• A. 250 K
• B. 250⁰C
• C. 2500 K
• D. 25⁰C

Answer 1

Answer: (A)

250 K

Answer 2

$P_{1} = P$, T₁ = T ,

$P_{2} = P +$ (0.4% of P)$= P + \frac{0.4}{100}P = P + \frac{P}{250}$ $T_{2} = T + 1$

From Gay Lussac's law $\frac{P_{1}}{P_{2}} = \frac{T_{1}}{T_{2}}$

⇒ $\frac{P}{P + \frac{P}{250}} = \frac{T}{T + 1}$ [As V = constant for closed vessel]

By solving we get T = 250 K.