Final Temperature of Carnot Heat Engine with Same U and N,C

[keith river]

Two bodies have the same Internal Energy. (U = N C T)
Both N and C are the same for each of these bodies. The initial Temperatures of these bodies are T1i and T2i

Using these bodies to produce work from a Carnot Heat Engine, they are brought to a final temperature Tf.

What is this final temperature in terms of the initial temperatures.

Looking at the problem since both internal energies have to be the same U1=U2 and N and C are the same for both bodies does this mean T1i = T2i if so doesn't that mean the final temperature would be equal to either of these temperatures?

However when I think of the first law of thermodynamics. (dU = dQ + dW) if the temperatures are the same does this mean dU = dW (No heat between objects of the same temperature) If so where would I go from here?

OR am I barking up the wrong tree completely.

 

[Andrew Mason]

Two bodies have the same Internal Energy. (U = N C T)
Both N and C are the same for each of these bodies. The initial Temperatures of these bodies are T1i and T2i

Using these bodies to produce work from a Carnot Heat Engine, they are brought to a final temperature Tf.

What is this final temperature in terms of the initial temperatures.

Looking at the problem since both internal energies have to be the same U1=U2 and N and C are the same for both bodies does this mean T1i = T2i if so doesn't that mean the final temperature would be equal to either of these temperatures?

However when I think of the first law of thermodynamics. (dU = dQ + dW) if the temperatures are the same does this mean dU = dW (No heat between objects of the same temperature) If so where would I go from here?

OR am I barking up the wrong tree completely.

There is no heat flow from or to the surroundings, so you are correct: $\Delta Q = 0; |\Delta U| = |W|$.

So what you have to do is figure out the amount of work produced during the operation of the engine to find the total change in internal energy. From that you can determine the final temperature.

AM