Question 657: Thermodynamics & KTG

Question

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 '. Assuming that the temperature ture of the gas remains constant during the leakage , the number of moles of the gas that have leaked is

Accepted Answer

Given:
Initial pressure of gas = $P$
Final pressure of gas after leakage = $P'$
Volume = $V$ (constant)
Temperature = $T$ (constant)
We need to find
the number of moles of gas that have leaked
.
Step 1: Write the ideal gas law
$ PV = nRT $
Where:
$P$ = Pressure
$V$ = Volume
$n$ = Number of moles
$R$ = Universal gas constant
$T$ = Temperature
Step 2: Calculate initial number of moles, $n_1$
$ n_1 = \frac{PV}{RT} $
Step 3: Calculate final number of moles, $n_2$ (after leakage)
$ n_2 = \frac{P'V}{RT} $
Step 4: Number of moles leaked
$ 	ext{Number of moles leaked} = n_1 - n_2 = \frac{PV}{RT} - \frac{P'V}{RT} $
$ = \frac{V}{RT}(P - P') $
Step 5: Match with the given options
The correct option is:
$ \boxed{\frac{V}{RT}(P - P')} $
So, the correct answer is Option B.

Answer

$\frac{2 \mathrm{~V}}{\mathrm{RT}}\left(\mathrm{P}-\mathrm{P}^{\prime}\right)$

Answer

$\frac{\mathrm{V}}{\mathrm{RT}}\left(\mathrm{P}-\mathrm{P}^{\prime}\right)$

Answer

$\frac{\mathrm{V}}{\mathrm{RT}}\left(\mathrm{P}+\mathrm{P}^{\prime}\right)$

Answer

$\frac{\mathrm{V}}{2 \mathrm{RT}}\left(\mathrm{P}+\mathrm{P}^{\prime}\right)$

Thermodynamics & KTG

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