Question

The kinetic energy per cubic metre of a perfect gas at N.T.P. is (Take atmospheric pressure = 1 x 105 N/m2)

1) 1.5 x 105 J/m3        2)  2 x 105 J/m3          

3)  0.75 x 105 J/m3     4)  2.5 x 105 J/m3


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Answer 1

question : The kinetic energy per cubic metre of a perfect gas at N.T.P. is.

1) 1.5 × 10^5 J/m³       2)  2 × 10^5 J/m³         

3)  0.75 × 10^5 J/m³     4)  2.5 × 10^5 J/m³

solution : according to kinetic theory of gas, P exerted by a gas of density ρ and r.m.s velocity v is given by, P = 1/3 ρv² .........(1)

and also average translational kinetic energy per unit volume is given by, E = 1/2 ρv² .......(2)

[ as kinetic energy , K.E = 1/2 mv² = 1/2 ρV v²

and then kinetic energy per unit volume, E = 1/2 ρv² ]

from equations (1) and (2) we get,

P/E = 2/3

⇒E = 3P/2 = 3 × 1 × 10^5/2 = 1.5 × 10^5 N/m²

Therefore kinetic energy per unit volume is 1.5 × 10^5 N/m² .