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A cylinder contained 10kgof gas at press...

A cylinder contained `10kg`of gas at pressure `10^(7) N / m^(2)`. The quantity of gas taken out of cylinder if final pressure is `2.5 xx 10^(6) N//m^(2)` is (Assume temperature of gas is constant)

A

7.5 kg

B

10.5 kg

C

5.2 kg

D

2.5 kg

Text Solution

Verified by Experts

The correct Answer is:
A
`P=(1)/(3)(M)/(V)v^(bar2)`, so, `PpropM`
where M = mass of the gas, V = volume and `v^(bar2)` = mean square speed of the gas molecules.
`therefore (P_(1))/(P_(2))=(M_(1))/(M_(2))orM_(2)=M_(1)(P_(2))/(P_(1))=10xx(2.5xx10^(6))/(10^(7))=2.5kg`
Quantity of gas taken out = `M_(1)-M_(2)=10-2.5=7.5kg`
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