Question

A sample of gas in a box is at pressure p0and temperature t0. If the number of molecules is doubled and total kinetic energy is kept constant the final temperature and pressure will be

Answer 1

Let number of molecules initially be n
Pressure be P0
Temprature be T0

Thus
As we know

P0V = nRT0
where   R  and V are constant

according to question

N= 2n
Thus

PV = 2nRT
n = PV / 2RT
Thus comparing we get
PV/2RT = P0V/RT0
Thus
P/2T = P0/T0

Answer 2

P0=1/3 mNvrms^2/V

If E0 is initial kinetic energy then

nE0=2nE

Kinetic energy of every molecules becomes half and T=T0/2

E=E0/2

E0=1/2 MV0^2

E=1/2 MV^2

V=vo/√2

P=1/3m2Nv0^2/2v

P=Po