A thermally insulated vessel with gaseous nitrogen at a temperature of `27^(@)C` moves with velocity `100 m//s^(-1)`. How much (in percentage) and in what way will the gas pressrue change if the vessel is brought to rest suddenly ?

Explanation

`(1)/(2) Mv^(2) = C_(v) Delta T = (R )/(gamma - 1) Delta T`
`(C_(V) = (R )/(gamma -1)) implies Delta T = ((gamma - 1) Mv^(2))/(2R)`
Now `pV = RT implies p = (RT)/(V) implies Delta p = (R )/(V) Delta T`
`:. (Delta p)/(p) = (((7)/(5) - 1) xx 28 xx 10^(-3) xx 100^(2))/(2 xx 8.3 xx 300)`
`= 0.0225 = 2.25%`