Question

Two cylinders A and B of equal capacity are connected to each other via a stopcock. A contains a gas at standard temperature and pressure. B is completely evacuated. The entire system is thermally insulated. The stopcock is suddenly opened.

Answer 1

Concept :- the entire system is thermally insulated . it means it is an isothermal process .
For an isothermal process temperature remains constant and it follows Boyle's law . I.e P1V1 = P2V2 .

For an isothermal process change in internal energy is zero.
I.e. ∆U = 0

Solution :-
(a) Let the volume of each cylinder is V and atmospheric pressure is P.
so, P1 = P
and V1 = V
When stopclock is opened , then volume available for gas becomes 2V
So, V2 = 2V
P2 = ?
A/C to Boyle's law,
P1V1 = P2V2
PV = P2 × 2V
P2 = P/2
But we know, atmospheric pressure = 1 atm so, P2 = 1atm/2 = 0.5 atm


(b) it is an isothermal process. So, change in internal energy is zero.
I.e. ∆U = 0

(c) change in temperature of the gas is zero due to no work in expansion .

(d) No, because free expansion of gas is rapid process and cannot be controlled . The intermediate state are non-equilibirium states also do not satisfy gases equation. So, the intermediate state of the gas doesn't lie on the P-V-T surface .