First slide

laws

Question

The Physical state of a gas is represented by P, V and T in Vessel A and 2P, $\frac{V}{4}$ 2T in vessel B. The ratio of number of molecules in A and B is

Easy

A

4 : 1
B

2 : 1
C

1 : 4
D

1 : 1

Solution

$P_{1} = P; P_{2} = 2 P; V_{1} = V; V_{2} = V / 4 T_{1} = T; T_{2} = 2 T$
We Know that,
$P V = μ R T P_{1} V_{1} = μ_{A} R T_{1} . . . . . . . . . . (1) P_{2} V_{2} = μ_{B} R T_{2} . . . . . . . . . . . (2)$
Taking ratio of Eq. (1) and Eq (2), we get,
$\frac{P_{1} V_{1}}{P_{2} V_{2}} = \frac{μ_{A} {RT}_{1}}{μ_{B} {RT}_{2}} \frac{P V}{2 P (V / 4)} = \frac{μ_{A} {RT}_{}}{μ_{B} R (2 T)} 2 = \frac{μ_{A}}{2 μ_{B}} \frac{μ_{A}}{μ_{B}} = \frac{4}{1} \Rightarrow μ_{A} = μ_{B} = 4 : 1$

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