Question

A thermally insulated vessel with gaseous nitrogen at a temperature T = ${27}^{\circ }$C moves with velocity v = 100 m/s.How much (in per cent) and in what way will the gas pressure changes on a sudden stoppage of the vessel.

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

Let the vessel contains one mole of gas.
$Here\frac{1}{2}m{v}^2=C_V\Delta T=\frac{fR}{2}\Delta T\Theta C_V=\frac{fR}{2}]\therefore \Delta T=\frac{2M{v}^2}{2fR}\text{From gas equation,}P=\left(\frac{RT}{V}\right)\text{Differentiating,}\Delta P=\frac{R}{V}\Delta T=\frac{P\Delta \Delta }{T}or\frac{\Delta P}{P}=\frac{\Delta T}{T}=\frac{M{v}^2}{fRT}=\frac{M{v}^2}{fRT}$
Substituting the values, we get
$\frac{\Delta P}{P}=\frac{(28\times {10}^{-3})(100{)}^2}{5\times 8.3\times 300}$
(f = 5 for diatomic gas)
= 0.022
Percentage change $=\frac{\Delta P}{P}\times 100$
$=0.022\times 100=2.2\%$