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laws

Question

A vessel contains 1 mole of O₂(molar mass 32) at a temperature T. The pressure of the gas is P. An identical vessel containing 1 mole of He gas (molar mass 4) at a temperature 2T has a pressure of

Easy

A

$\frac{P}{8}$
B

P
C

2P
D

8P

Solution

It is given that
$P_{1} = P V_{2} = V μ_{1} = 1 T_{2} = 2 T T_{1} = T μ_{2} = 1 V_{1} = V P_{2} = ?$
We know that
$PV = μRT P_{1} V_{1} = μ_{1} RT P_{2} V_{2} = μ_{2} {RT}_{2}$
Dividing Eq.(1) by Eq. (2), We get
$\frac{P_{1} V_{1}}{P_{2} V_{2}} = \frac{μ_{1} {RT}_{1}}{μ_{2} {RT}_{2}} \frac{P}{P_{2}} x \frac{V}{V} = \frac{1 xT}{1 x 2 T} \Rightarrow P_{2} = 2 P$

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