Question

As insulated container is divided into two equal portions. One portion contains an ideal gas at pressure P and temperature T, while the other portion is a perfect vacuum. If a hole is opened between the two portions, find the change in internal energy and temperature of the gas.

• A.
• B.
• C. infinite

Answer 1

As the system is thermally insulated,
$\Delta$Q = 0
Further as here the gas is expanding against vacuum (surroundings), the process is called free expansion and for it,
$\Delta W=\int PdV=0\text{[as for vacuum P = 0]}$
So in accordance with first law of thermodynamics, i.e. $\Delta Q=\Delta U+\Delta W$, we have
0 = $\Delta$U + 0,
i.e. $\Delta$ U + 0 or U = costant
So in this problem internal energy of the gas remains constant, i.e. $\Delta$U =0. Now as for an ideal gas
$U=\frac{3}{2}\mu RT$, i.e. U $\propto$ T
So temperature of the gas will also remain constant, i.e. $\Delta T=0$