- 66

- 0

**1. Homework Statement**

An object maintained at constant volume has heat capacity Cv, which is independent of T. The object is initially at a temperature Th, and a heat reservior at a lower temperature Tc is available. Show that the maximum work that can be extracted when a heat engine operating between the object and the reservior brings the object to the temperature of the reservior is

W = Cv [ (Th - Tc) - Tcln (Th/Tc) ].

Hint, the maximum amount of work is obtained when the process is rversible, i.e., when the entropy change of the universe is zero.

Solve the previous problem if the cold reservior is replaced by an object of heat capacity Cv. Hint: First find the final temperature of the two objects.

**2. Homework Equations**

**3. The Attempt at a Solution**

W=Qh-Qc

dQ=mCvdT--> Q=mCv(Tf-Ti)

I can see how the first part of the expression came about by integraing dQ and considering Tf as Th and Ti as Tc, but I dont get where the natural log came in since i dont know where a 1/T term would come in...