# Multiple Choice problem (internal energy)

cathole
What must be true for two objects of the same material to have the same internal energies?
(Choose all that apply)

a. The masses of both objects must be equal

b. Both objects must have the same density

c. The temperatures of both objects must be equal

d. Separate objects cannot have identical internal energies

I guessed a,b,c and was wrong. I am thinking only a &b. Please tell me what you think.

Homework Helper
You aren't saying why you think any of those are true. Guessing may be the wrong strategy. How would you calculate internal energy of a system given temperature and masses of the component objects, assuming it's an ideal gas for example?

cathole
Dick,
I have no clue what "strategy" to go with, that's the whole reason I'm here.

Homework Helper
Dick,
I have no clue what "strategy" to go with, that's the whole reason I'm here.

Right, but can you think of two objects whose masses are equal but have different internal energies? Two objects whose densities are equal but have different internal energies etc. etc. That's the sort of strategy I'm talking about. Are ANY of those true? All I know is guessing won't work. They wouldn't give you this question if you didn't know SOMETHING.

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Homework Helper
You've got the right general idea about what internal energy is, that's a start. But try and make that general idea more concrete. Don't you have ANY specific examples to reason from? Like I said ideal gases would be a good starting point. But why do you think temperature doesn't matter? Doesn't that determine internal kinetic energies and vibrational energies? Are you really supposed to answer this starting from ground zero?

cathole
Yes, ground zero. I am leaning towards mass and temperature as the answer to the question.

cathole
I will have two lectures on thermodynamics in the coming week. I'm trying to complete online homework and can't find a good source of information for this question.

cathole
I think I've got it.

The objects have to have the same mass in order to have equal heat capacity.

The objects have to have the same temperature to be in thermal equilibrium.

If there heat capacity and thermal equilibrium are identical, their internal energy will be the same.

Homework Helper
I think I've got it.

The objects have to have the same mass in order to have equal heat capacity.

The objects have to have the same temperature to be in thermal equilibrium.

If there heat capacity and thermal equilibrium are identical, their internal energy will be the same.

No, that's not it. If sample A has internal energy E, and sample B has internal energy 2E, then two copies of A have the same internal energy as B, right? Internal energy is an extensive property, yes? Do A and B have to have any properties in common?

cathole
Here it is...

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