Consider two identical bodies of heat capacity CP and with negligible thermal ex
ID: 2238280 • Letter: C
Question
Consider two identical bodies of heat capacity CP and with negligible thermal expansion coefficients. Show that when they are placed in thermal contact in an adiabatic enclosure their final temperature is (T1 + T2)/2 where T1 and T2 are their initial temperatures. Now consider these two bodies being 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 reservoirs during one cycle. Show that the final temperature is (T1 T2)1/2. (Hint: What is the entropy change of the universe for this second process?)Explanation / Answer
part(1),let T1>T2, heat taken = heat rejected, m.Cp.(T1-T)=m.Cp.(T-T2), simplifying,we get, T=(T1 +T2)/2,(ANSWER), part(2), in case of carnot cycle, entropy of universe is zero as process is reversible, dS1 + dS2 =0, integral of [Cp.(dT/T)] (limit, T1,T) + integral of [Cp.(dT/T)](limit, T2,T) =0, Cp[ln(T/T1) + Cp[ln(T/T2)] =0, simplifying we get, T = sqrt(T1.T2) (ANSWER).