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Thermodynamics — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysicsThermodynamics3 Marks
Question
A certain gas at atmospheric pressure is compressed adiabatically so that its volume becomes half of its original volume. Calculate the resulting pressure in Nm-2. Take $\gamma=1.4$ for air.
✓

Answer

Let the original volume,
V1 = V
$\therefore$ Final valume,
$\text{V}_2=\frac{\text{V}}{2}$
Initial pressure,
P1 = 0.76 metre of Hg column.
Let P2 be the fanal pressure after compression.
As the change is adiabatic,
$\therefore\text{P}_1\text{V}_1^\gamma=\text{P}_2\text{V}_2^\gamma$
$\text{P}_2=\text{P}_1\Big(\frac{\text{V}_1}{\text{V}_2}\Big)^\gamma=\text{P}_1\bigg(\frac{\text{V}}{\frac{\text{V}}2{}}\bigg)^{1.4}$
$\text{P}_2=0.76\times(2)^{1.4}$
$\text{P}_2=2.00$ metre of Hg column,
As $\text{P}=\text{h}\rho\text{g}$
$\therefore\text{P}_22.00\times(13.6\times10^3)\times9.8\text{ Nm}^{-2}$
$\text{P}_2=2.672\times10^5\text{Nm}^{-2}$

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