MHT CET 2021 Physics Solved Paper

(d) The rms velocity of gas molecule,
vrms‌‌=√‌

3RT

m

‌ As, ‌‌‌K‌‌=‌

1

2

mvrms2
‌‌=‌

1

2

m(‌

3RT

m

)=‌

3

2

RT
⇒‌‌K‌‌=‌

3

2

RT‌‌‌⋅⋅⋅⋅⋅⋅⋅(i)
From ideal gasequation for one mole,
pV=RT‌‌‌⋅⋅⋅⋅⋅⋅⋅(ii)
From Eqs. (i) and (ii), we get,
p=‌

2

3

‌

K

V

Hence, pressure is (‌

2

3

) rd of kinetic energy per unit volume of gas.