Question

Assuming the expression for the pressure p exerted by an ideal gas ,prove that the kinetic energy per unit volume of gas is 3/2p.

Answer 1

Explanation:

Correct option is

B

[

3

2

]

rd

kinetic energy per unit volume of a gas

Kinetic energy of the gas K=

2

1

mv

rms

2

Rms velocity of gas molecules v

rms

=

m

3RT

∴ K=

2

1

m.

m

3RT

=

2

3

RT

From ideal gas equation, RT=PV

⟹ K=

2

3

PV

Thus we get pressure of the gas P=

3

2

V

K