Question

An ideal gas is kept in a long cylindrical vessel fitted with a frictionless piston of cross-sectional area 10 $c{m}^2$ and weight 1 kg. The length of the gas column in the vessel is 20 cm. The atmospheric pressure is 100 kPa. The vessel is now taken into a spaceship revolving round the earth as a satellite. The air pressure in the spaceship is maintained at 100 kPa. Find the length of the gas column in the cylinder.

Answer 1

$P_1{V}_1=P_2{V}_2$

$\Rightarrow (\frac{mg}{A}+P_0)Al=P_{0}A{l}^{\prime }$

$\Rightarrow (\frac{1\times 98}{10\times {10}^{-4}}+{10}^5)0.2={10}^5{l}^{\prime }$

$\Rightarrow (9.8\times {10}^3+{10}^5)\times 0.2={10}^5{l}^{\prime }$

= $109.8\times {10}^3\times 0.2={10}^5{l}^{\prime }$

$\Rightarrow l^{\prime }=\frac{109.8\times 0.2}{{10}^2}$

= 0.2196 m = 0.22 m $\approx$ 22 cm