Question

An ideal gas is kept in a long cylindrical vessel fitted with a frictionless piston of cross-sectional
area 10 cm² 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

$\begin{array}{l}\text{Here,}\\ V=50m^3\\ T=273+15=288K\\ RH=40\%\\ a)\\ \text{Let x be the amount of water that evaporates.}\\ \text{P=RH}\times \text{SVP}\\ \text{⇒P=0}\text{.4}\times \text{1600=640}\\ PV=\frac{m}{M}RT\\ \Rightarrow m=\frac{PVM}{RT}=\frac{640\times 50\times 18}{8.3\times 288}=241g\\ \text{Water will evaporate until VP becomes equal to SVP.}\\ \Rightarrow 1600\times 50=\frac{m+x}{M}RT\\ \Rightarrow 1600\times 50=\frac{241+x}{18}\times 8.3\times 288\\ \Rightarrow x\approx 361\text{g}\\ \text{b)}\\ T=288+5=293K\\ SVP=2400\text{Pa}\\ \text{Difference in pressure =}2400-1600=800\text{Pa}\\ \\ \\ \text{Let x be the amount of water that evaporates.}\\ PV=\frac{x}{M}RT\\ \Rightarrow 800\times 50=\frac{x}{18}\times 8.3\times 293\\ \Rightarrow x\approx 296\text{g}\end{array}$