If one mole of {H}_{2} gas occupies a rigid container with a capacity of 1000 litres and the temperature is raised from 27^{\circ} {C} to 37^{\circ} {C}, the change in pressure of the contained gas (round off to two decimal places), assuming ideal gas behaviour, is

GATE Mechanical Engineering (ME) 2019 Shift 1 Solved Paper

Question : 42 of 65

Marks: +1, -0

If one mole of

{H}_{2}

gas occupies a rigid container with a capacity of 1000 litres and the temperature is raised from

27^{∘} {C}

37^{∘} {C}

, the change in pressure of the contained gas (round off to two decimal places), assuming ideal gas behaviour, is

Solution:

From ideal gas equation, pV = mRT
Or,

p V=n \ov{R} T

So,

p × 1=1 × 8.314 × 300 \;\; [1000

litres

=1 {m}^{3} {/} {s}

]

So,

p=2494.2 {Pa}

Container is rigid, so

∆ V=V_{2}=V_{1}

Using,

\;{P_{1}}/{T_{1}}=\;{P_{2}}/{T_{2}}

⇒ P_{2}=\;{2494.2 × 310}/{300}=2577.34 P a

Therefore,

∆ P=P_{2}-P_{1}=2577.34-2494.2=83.14 {Pa}

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