Three identical bodies of constant heat capacity C = 10 J/K are initially at tem

Question

Three identical bodies of constant heat capacity C = 10 J/K
are initially at temperatures of 300, 300, and 100 K. The bodies can interact with each other and
with their surroundings only by exchanging heat with one or more heat engines, and no net work
or heat is available from outside sources. (Thus, in particular, you may extract work from a heat
engine operating between two of the bodies, store it, and use it later, but you cannot put back in
more work than you got out.)

What is the highest temperature to which any one of the bodies can be raised? (That is,
you’re trying to get one of the bodies—whichever one you choose—to as high a temperature
as possible, but you don’t care about the temperatures of the other two. How high can you
get?

Explanation / Answer

Heat energy possessed by 100K body = m*C*100

by the 300 K bodies = m*C*100

Let the whole thermal energy possessed by one of the 300K body and the 100K body be transferred to the other 300K body

So, the total energy of the 300 K body = m*C*300 + m*C*300+ m*C*100 = m*C*700

So, the tempereaure can go as high as 700 K

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