Areal heat engine operates between temperatures tc and th. during a certain time, an amount qc of heat is released to the cold reservoir. during that time, what is the maximum amount of work wmaxthat the engine might have performed? express your answer in terms of qc, th, and tc.

Qc * (1 - Th/Tc)

Explanation:  

Maximum Work done = Qh * η

                                Wmax  = Qh * (1 - Tc/Th)

For reversible cycle of engine: Qc/Tc + Qh/Th = 0

                                                   Qh = -(Qc*Th)/Tc

Substituting Qh back into equation for work:

Wmax = -(Qc*Th)/Tc *  (1 - Tc/Th)

Wmax = -(Qc*Th)/Tc + Qc

Wmax = Qc * (1 - Th/Tc)

3.2x10^7

nah.   i'm just sleepy.