Physics: Two unequal masses of iron both have the same Internal energy, which of the following is true?

Question

Two unequal masses of iron both have the same Internal energy, which of the following is true?

 

a. The larger mass is hotter

b. The smaller mass is hotter

c. The have the same temperature

Answer 1

The smaller one is hotter.   Internal energy is an extensive quantity (scales with the size of the system every thing else being the same), while temperature is an intensive parameter (will not change if the system is divided into parts). 

Suppose that the mass of the larger iron is  1.5 kg and the mass of the small iron is 1 kg.   If a chunk of mass 1 kg is removed from the large iron, it would have less  (by 1/3) internal energy than the original small iron, but would still be at the original temperature of the large iron.  After this operation, we would have two pieces of mass 1 kg with unequal internal energies.   Since internal energy is a monotone increasing function of temperature, the masses cannot be at the same temperature.  This rules out answer c).   By the same token, the temperature of the removed chunk must be cooler since it has less internal energy than the equal mass original smaller mass. 

Answer 2

I would say the answer is b.