A container of volume V contains n moles of gas at high pressure. Connected to the container is a capillary tube through which the gas may leak slowly out to the atmosphere, where the pressure is Po.
Surrounding the container and capillary is a water bath, in which is immersed an electrical resistor. The gas is allowed to leak slowly through the capillary into the atmosphere while electrical energy is dissipated in the resistor at such a rate that the temperature of the gas, the container, the capillary, and the water is kept equal to that of the outside air. Show that, after as much gas as possible has leaked out during time interval t, the change in internal energy is
ΔU = εIt - P0(nv0 - V),
Where Vo is the molar volume of the gas at atmospheric pressure, ε is the potential difference across the resistor, and I is the current in the resistor.