A gas is filled in a cylinder. Its temperature is increased by 20 % on the Kelvin scale and volume is reduced by 10 % . How much percentage of the gas has to leak for pressure to remain constant?

Question

A gas is filled in a cylinder. Its temperature is increased by 20 % on the Kelvin scale and volume is reduced by 10 % . How much percentage of the gas has to leak for pressure to remain constant? (A) 30 % (B) 40 % (C) 15 % (D) 25 %

Tardigrade Admin · Accepted Answer

V propto μ T,(90/100) V propto μ â²(6 T/5) (μ â²/μ )× (6/5)=(9/10) or(μ â²/μ )=(9/10)× (5/6)=(3/4) Percentage of gas leaked out =(μ - μ â²/μ )× 100=(4 - 3/4)× 100=25 %

Q. A gas is filled in a cylinder. Its temperature is increased by $20%$ on the Kelvin scale and volume is reduced by $10%$ . How much percentage of the gas has to leak for pressure to remain constant?

$30%$

$40%$

$15%$

$25%$

$V \propto μ T, \frac{90}{100}$ $V \propto μ^{'} \frac{6 T}{5}$
$\frac{μ ^{'}}{μ} \times \frac{6}{5} = \frac{9}{10} or \frac{μ ^{'}}{μ} = \frac{9}{10} \times \frac{5}{6} = \frac{3}{4}$
Percentage of gas leaked out
$= \frac{μ - μ '}{μ} \times 100 = \frac{4 - 3}{4} \times 100 = 25$ $%$

Q. A gas is filled in a cylinder. Its temperature is increased by 20% on the Kelvin scale and volume is reduced by 10% . How much percentage of the gas has to leak for pressure to remain constant?

30%

40%

15%

25%