MHTCET 13 May 2023 Shift 2 Solved Paper

Pressure p of the gas is given by,
p=‌

1

3

‌

mN

V

vrms2
Where, m is mass, N is the number of moles, V is the volume and vrms is the root mean square velocity of the particles of the gas.
∴‌‌p1=p0=‌

1

3

‌

m1N

V1

(v‌rms ‌2)1.....(i)
If m2=‌

m1

2

and (vrms)2=2(vrms)1
For simplicity write v2=2v1
Hence, p2=‌

1

3

‌

m2N

V

v22....(ii)
Divide Eq. (i) by Eq. (ii)
‌‌

p0

p2

=‌

‌ 1 3 m1N V v12

1 3 ‌ m2N V v22

‌⇒‌‌‌

p0

p2

=‌

m1v12

m1 2 (2v1)2

⇒‌

p0

p2

=‌

1

2

‌⇒‌‌p2=2p0
∴ Resulting pressure is 2p0