An ideal gas system changes from state i to state f by paths iaf and ibf. If the heat added along iaf is Q_iaf = 50 cal, the work along iaf is W_iaf = 20 cal. Along ibf, if Q_ibf = 40 cal, the work done, W_iaf, is

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The first law of thermodynamics states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. Using this law, we can determine the change in internal energy along iaf: ΔUiaf = Q_iaf - W_iaf = 50 cal - 20 cal = 30 cal Since internal energy is a state function, the change in internal energy along ibf must be equal to ΔUiaf: ΔUibf = ΔUiaf = 30 cal Using the first law of thermodynamics, we can then calculate the work done along ibf: W_ibf = Q_ibf - ΔUibf = 40 cal - 30 cal = 10 cal Therefore, the answer is B) 20 cal.

An Ideal Gas System Changes from State I to State