Answer to Question #214473 in Molecular Physics | Thermodynamics for Wavie

Question

A vessel of volume 0.2m3 contains nitrogen at 1.013 bar and 15°C. If 0.2 kg of nitrogen is now pumped into the vessel, calculate the new pressure when the vessel has returned to its initial temperature. The molar mass of nitrogen is 28 kg/K - mol and it may be assumed to be a perfect gas.

Answer 1

Solution.

$V=0.2m^3;$

$p_1=1.013\sdot10^5Pa;$

$T=288K;$

$m_2=0.2kg;$

$M=28\sdot10^{-3}kg/mol;$

$p_2V=\dfrac{m_2}{M}RT\implies p_2=\dfrac{m_2RT}{MV};$

$p_2=\dfrac{0.2\sdot8.31\sdot288}{28\sdot10^{-3}\sdot0.2}=0.855\sdot10^5Pa;$

$p=p_1+p_2;$

$p=1.013\sdot10^5Pa+0.855\sdot10^5Pa=1.868\sdot10^5Pa;$

Answer: $p=1.868$ bar.