Two thermally insulated vessels are interconnected by a tube equipped with a valve. One vessel volume `V_1 = 10 1` contains `v = 2.5` moles of carbon dioxide. The other vessel of volume `V_1 = 100 1` is evacuated. The valve having been opened, the gas adiabatically expanded. Assuming the gas to obey the Van der Walls equation, find its temperature change accompanying the expansion.

Explanation

From the first law
`Q = U_f - U_i + A = 0`, as the vessels are themally insulated.
As the is free expansion, `A = 0`, so, `U_f = U_i`
But `U = v C_V T - (av^2)/(V)`
So, `C_V(T_f - T_i)= ((a)/(V_1 + V_2)-(1)/(V_1)) v = (-a V_2 v)/(V_1(V_1 + V_2))`
or, `Delta T = (-a(gamma - 1)V_2 v)/(RV_1(V_1 + V_2))`
Substitution gives `Delta T = -3 K`.