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Q.

A closed vessel A having volume V contains N₂ at pressure P and temperature T. Another closed vessel B having the same volume V contains He at the same pressure P but temperature 2T. The ratio of masses of N₂ and He in the vessels A and B is:

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a

1 : 2

b

3 : 2

c

5 : 2

d

14 : 1

answer is D.

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Detailed Solution

PV = nRT

Rightarrow PV = left( {nM} right)frac{{RT}}{M} = mfrac{{RT}}{M}

Rightarrow m = frac{{PV}}{R}frac{M}{T}

So at same pressure and volume,

m propto frac{M}{T}

$∴ \frac{{m_{N}}_{2}}{m_{H e}} = \frac{M_{N_{2}}}{M_{H e}} \times \frac{T_{H e}}{T_{N_{2}}}$

= frac{{28}}{4} times 2 = 14

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A closed vessel A having volume V contains N2 at pressure P and temperature T. Another closed vessel B having the same volume V contains He at the same pressure P but temperature 2T. The ratio of masses of N2 and He in the vessels A and B is: