Question

A gas is confined to a sub-volume V1 in an insulated rigid container. The container has an adjoining sub-volume V2, initially evacuated(vacuumed), which can be connected to V1 by opening a valve. V1=V2. Suppose the valve is opened and the gas flows out of V2, filling the entire volume V1+V2. Assume the specific gas constant is R.

                a)Calculate the work done by the gas in this expansion.

                b) Calculate the change in internal energy of the gas.

                c) Calculate the change in entropy of the gas.

                d) Is the process adiabatic? Is it isothermal? Is it reversible?

The final answers to (a)-(c) are in V1 and R, not specific values.

For all equations I would really appreciate it if you could explain source of any root equations used. Thanks!

Answer 1

a) Since the gas is expanding into the sub-volume V2 which is initially evacuated, it is a free expansion (external pressure = 0 as V2 is vaccum).

work done for free expansion = 0

Hence, work done by the gas in this expansion = 0

b) Since the container is insulated and rigid, there is no heat exchange.

q = 0

As it is free expansion, w = 0

Therefore,

Hence, change in internal energy of the gas = 0.

c) For an insulated system, there is no interaction between system and surrounding.

So,

For free expansion,

Since, V₁ = V₂

Hence, the total change in etropy is nR(ln2).

Where n is number of moles of the gas and R is gas constant.

d) The process is an isothermal process. It is isothermal free expansion.