Question

A gas taken in a closed vessel is heated from 54°C to 1254°(C) The pressure of the gas becomes __________ times its original pressure \( P_1 \).

• A. 8.92 times \( P_1 \)
• B. 23.2 times \( P_1 \)
• C. 4.67 times \( P_1 \)
• D. 9.6 times \( P_1 \)

Hint:

Gay-Lussac's law states that the pressure of a fixed amount of gas is directly proportional to its temperature (in Kelvin) when the volume is held constant.

Answer 1

The Correct Option is C

We are given the following data: - Initial temperature, \( T_1 = 54^\circ C = 54 + 273 = 327 \, K \) - Final temperature, \( T_2 = 1254^\circ C = 1254 + 273 = 1527 \, K \) - The pressure of the gas is directly proportional to the temperature when the volume is constant, according to Gay-Lussac's Law: \[ \frac{P_2}{P_1} = \frac{T_2}{T_1} \] Now substituting the values: \[ \frac{P_2}{P_1} = \frac{1527}{327} = 4.67 \] Thus, the pressure of the gas becomes \( \mathbf{4.67} \) times its original pressure \( P_1 \).