[Lamprey5 (OP)]

In my IB Physics homework, a question was asked:
If an object is split in half, what happens to the internal energy and temperature of each half?
The answer (from the back of the textbook) is that the internal energy of each half is 1/2 of the internal energy of the original object. The temperature of each half is the SAME as that of the original object.

In the lessons, the book says: An object's temperature (a macroscopic property) is directly proportional to the amount of internal energy (a microscopic property) it has in its molecules/atoms. The internal energy is the total kinetic energy of the molecules of a substance + any potential energy associated with intermolecular (not INTRA-molecular, such as ionic and covalent bonds) forces.

My problem: I understand how the internal energy has changed. The total kinetic energy of the molecules in each half is 1/2 of the EK in the original object (since there are half as many particles moving around). Therefore shouldn't the temperature of each half be halved as well?

[Soul Surfer]

No! the temperature is not defined as the total internal energy of the object but the mean internal energy of each atom or molecule in the object so dividing it in half has no effect on the temperature.