Internal energy of an ideal gas as a function of temperature

[eprparadox]

Homework Statement

Two containers hold an ideal gas at the same temperature and pressure. Both containers hold the same type of gas but container B has twice the volume of container A.

The internal energy of the gas in container B is
(a) twice that for container A
(b) the same as that for container A
(c) half that for container A
(d) impossible to determine.

Homework Equations

$$U = \frac{1}{2}Nfk_BT$$

The Attempt at a Solution

I'm doing some self study and I'm confused here. For ideal gases, the internal energy is suppose to be a function of temperature only. So I would think the answer is b.

The answer in the book says "(a) Because there are twice as many molecules and the temperature of both containers is the same, the total energy in B is twice that in A."

What am I missing?

 

[I like Serena]

Hi eprparadox!

As your relevant equation shows, the (total) internal energy is also a function of the number of molecules.
It's only if we're talking about energy per mole, which is often the case, that this dependency is 'divided out'. But in this case we are talking about the total energy.

 

[eprparadox]

Hey, awesome thanks so much I like Serena!