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A gas of mass m, is filled in a vessel at 7degree celsius.if x fraction of its mass escapes out at 27 degree celsius
find x. (Assuming pressure constant).
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Answer 1

The value of x is  x = (1 / 14)V.

Explanation:

• Let Volume of gas at 7°C = V1 = V
• Volume of gas at 27°C = V2

[Since the pressure is constant]

• According to Charles' law

V1 / T1 = V2 / T2

V/(273+7) = V2/(273+27)

V2 = 300 V/280 = 15 V/14

• Now Putting the value of  V2 = V+x

V+x=15 V/14

x=15 V/14-V

x=(1/14).V  

x=1/14 of total volume of the gas (vessel).

Thus the value of x is  x=(1/14)V.

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Answer 2

The value of x is (1/14) of total volume of gas.

Explanation:

Volume of gas at 7°C = V₁

7°C = 273+7 = 280 K = T₁

Volume of gas escapes at 27°C = x

Volume of gas at 27°C after escape = V₂ = V₁ + x

27°C = 273+27 = 300 K = T₂

V₁/T₁ = V₂/T₂

Now, on substituting the given values, we get,

V₁/280 = (V₁ + x)/300

V₁ + x = (300 V₁)/280 = (15 V₁)/14

x = (15 V₁)/14 - V₁

x = (15 V₁ - 14 V₁)/14

∴ x = (1/14) V₁

Thus, mass of gas escaped at 27°C is (1/14) of total volume of gas.