Q120 / 150 · MHT CET 2026 (19 April Shift 2) · Physics
An ideal gas at pressure 'P' and temperature 'T' is enclosed in a vessel of volume 'V'. Some gas leaks through a hole from the vessel and the pressure of the enclosed gas falls to $P^1$. Assuming that the temperature of the gas remains constant during the leakage, the number of moles of the gas that have leaked is
- A$\dfrac{P^1 V}{RT}$
- Correct answerB$\dfrac{V}{RT}(P - P^1)$
- C$\dfrac{2V}{RT}(P + P^1)$
- D$\dfrac{V}{RT}(P + P^1)$
Solution
Initial number of moles of the gas is given by the ideal gas equation:
$n_1 = \dfrac{PV}{RT}$
After the leakage, the final number of moles of the gas is:
$n_2 = \dfrac{P^1V}{RT}$
The number of moles of the gas that have leaked is:
$\Delta n = n_1 - n_2$
$\Delta n = \dfrac{PV}{RT} - \dfrac{P^1V}{RT}$
$\Delta n = \dfrac{V}{RT}(P - P^1)$
Answer: $\dfrac{V}{RT}(P - P^1)$
$n_1 = \dfrac{PV}{RT}$
After the leakage, the final number of moles of the gas is:
$n_2 = \dfrac{P^1V}{RT}$
The number of moles of the gas that have leaked is:
$\Delta n = n_1 - n_2$
$\Delta n = \dfrac{PV}{RT} - \dfrac{P^1V}{RT}$
$\Delta n = \dfrac{V}{RT}(P - P^1)$
Answer: $\dfrac{V}{RT}(P - P^1)$
Hence, the correct answer is option: 'B'.