Consider an ideal gas with N = 1023 particles and an internal energy of U = 100 J. If the gas triples in volume, but its entropy remains constant, what is the internal energy after it expands? Hint: write the new energy as aU, and solve for a.

Explanation:

This is a trick question!

The intenal energy is the total heat energy stored in the system. The only factor that affects the internal energy of a system is the temperature. If during heating the temperature increases it’s internal energy also increases and it decreases when the temperature decreases.

This means the gas tripling in volume and entropy being consant have no effect whatsoever on the internal energy. The internal energy of the system, U remains 100J.