# Thermodynamics - Carnot engine

1. Oct 30, 2008

### ronny45

1. The problem statement, all variables and given/known data

Consider 2 identical bodies of constant heat capacity Cp and with negligble termal expansion coefficients. Initial temperatures are T1 and T2.
a) When they are placed in thermal contact in an adiabatic enclosure, what is their final temperature?
b) The 2 bodies are brought to thermal equilibrium by a Carnot engine operating between them. The size of the cycle is small so that the temperatures of the bodies do not change appreciably during one cycle; thus the bodies behave as resevoirs during one cycle. Show that the final temperature is sqrt(T1T2). Hint: What is the entropy change of the universe for this second process?
(Assume isobaric conditions throughout, and T2>T1).

3. The attempt at a solution
a) seems fairly straight-foward... if the enclosure is adiabatic, there's no heat exchange between the system and the surroundings, so the final temperature = (T1+T2)/2.

b) I really don't know where to start on this one, i've been at it over a week and i'm none the wiser. The hint is only confusing me because i was under the impression that entropy, as a state function, would not change over one cycle. How does this help me?