What amount of heat has to be transferred to `v = 3.0` moles of carbon dioxide to keep its temperature constant while it expands into vacuum from the volume `V_1 = 5.0 1` to `V_2 = 10 1` ? The gas is assumed to be a Van der Walls gas.

Explanation

`Q = U_f - U_i + A = U_f - U_i`, (as `A = 0` in free expansion)
So at constant temperature.
`Q = (-av^2)/(V^2) -(-(av^2)/(V_1)) = av^2 (V_2 - V_1)/(V_1 .V_2)`
=`0.33 kJ` from the given data.