A thermally insulated vessel with nitrogen gas at 27^ C is moving with a velocity of 100 ~ms ⁻¹ . If the vessel is stopped suddenly, then the percentage change in the pressure of the gas is nearly (assume entire loss in KE of the gas is given as heat to gas and R=8.3 Jmol ⁻¹ ~K ⁻¹ )

Step-by-step solution

Let there are n moles of N₂ gas in the cylinder. Assuming all of K, E appears in form of heat, n ( 1 2 M v^2 )= f 2 n R T Here, M=28 ~g =28 10⁻³ ~kg , f=5 Increment in pressure due to change of temperature is Also, p= n R T V So, p p = ( n R T V ) ( n R T V ) = n R T n R T p p = n M v^2 f n R T = M v^2 f R T So, percentage change in pressure is, p p 100= 28 10⁻³ 100 100 5 8.3 300 100=2.25 %