CGPET 2019 Solved Paper

Let mass of molecule m and speed v, then by kinetic theory of gasses,
∴PV=

1

2

nmv2 ......(i)
Here, P= initial pressure
and V= initial volume.
According to question,
Mass of molecules of gas =

m

2

and Speed of the gas molecules =2v.
Then,
P′V′=

1

3

n(

m

2

)(2v)2
Here, P′ is final pressure of gas molecules.
or, P′V′=

1

3

n

m

2

×4v2
or P′V′=

1

3

nm×2v2 ......(ii)
Now from equation (i) and (ii), we get
or,

PV

P′V′

=

1 3 nmv2

1 3 nmv2×2

or,

P

P′

=

1

2

(∵v=v′)
So, the ratio of Initial and final pressure is 1:2.