In an exam, I had a scenario where 2 bodies with different temperatures were put together and over time their temperatures mixed and eventually became uniform. My intuition tells me that as a result, the entropy of this system increased, however the exam asked me to explain why entropy remained the same. Could someone tell me whether the exam is correct, and if so, why?
Edit: The problem was posted on our website (with no official answer unfortunately), so here it is in full:
Consider an isolated system composed of two bodies at slightly different temperatures T1 and T2 (T1 = T2 + dT) thas have been put in contact. a) What does the second law of thermodynamics say about the direction of heat flow between them? (1pt) b) Explain how the entropy of both bodies change. Show that the total entropy of that system is constant. (6pts)
(there's a picture showing the 2 bodies and a barrier around them labeled "perfect insulation")