A bomb of volume  contains n mole of gas at high pressure

A bomb of volume  contains n mole of gas at high pressure. A capillary tube is connected to the bomb, through which the gas may slowly leak out into the atmosphere, where the pressure is . Bomb and capillary are immersed in the water bath in which heat is added through the electric resistor. Now the gas is allowed to leak slowly through the capillary tube into the atmosphere and at the same time electric energy is dissipated in the resistor in such a rate that temperature of the gas, the bomb, the capillary and water is kept equal to that of the outside air.
Show that after as much gas as possible has leaked out during time ‘’, the change of internal energy is,

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