Question

5 $d{m}^3$ volume of a gas exerts a pressure of $2.02\times {10}^{5}kPa$. This gas is completely pumped into another tank where it exerts a pressure of $1.01\times {10}^{5}kPa$ at the same temperature, Calculate the volume of the tank.

Answer 1

Given, Volume initially=$5d{m}^3$

Pressure initially=$2.02\times {10}^{5}KPa$

Pressure finally=$1.01\times {10}^{5}KPa$

Volume finally=$x$

According to Boyle's Law, at constant temperature

$P\propto \frac{1}{V}$

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

$\therefore V_{final}=\frac{P_i\times V_i}{P_f}$

$V_{final}=\frac{2.02\times {10}^{5}KPa\times 5d{m}^3}{1.01\times {10}^{5}KPa}$

$=10d{m}^3$

$\therefore$ Volume of final tank=$10d{m}^3$