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Standard VIII

Physics

Expansion of Gases

If at 60∘C ...

Question

If at $60^{\circ}$ C and $80 cm$ of mercury pressure, a definite mass of a gas is compressed slowly, then the final pressure of the gas if the final volume is half of the initial volume $(γ = \frac{3}{2}$ ) is:

120 cm of Hg

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140 cm of Hg

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160 cm of Hg

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180 cm of Hg

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Solution

The correct option is C $160 cm of Hg$
Given initial pressure, $P_{1} = 80 c m o f H g$

If the gas is compressed slowly, then the process is isothermal.

At constant temperature,

$P_{1} V_{1} = P_{2} V_{2}$

Given,

Final volume is half of the initial volume.

That is, $V_{2} = \frac{V_{1}}{2}$

Final pressure, $P_{2} = \frac{P_{1} V_{1}}{V_{2}} = \frac{80 \times V_{1}}{V_{1} / 2} = 160 c m o f H g$

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If at 60∘C and 80 cm of mercury pressure, a definite mass of a gas is compressed slowly, then the final pressure of the gas if the final volume is half of the initial volume (γ=32) is:

The correct option is C 160 cm of HgGiven initial pressure, P1=80cmofHgIf the gas is compressed slowly, then the process is isothermal.At constant temperature,P1V1=P2V2Given, Final volume is half of the initial volume.That is, V2=V12Final pressure, P2=P1V1V2=80×V1V1/2=160cmofHg

If at $60^{\circ}$ C and $80 cm$ of mercury pressure, a definite mass of a gas is compressed slowly, then the final pressure of the gas if the final volume is half of the initial volume $(γ = \frac{3}{2}$ ) is: