Internal energy of an ideal gas as a function of temperature

In summary, the internal energy of a gas is a function of both temperature and the number of molecules present. In the given scenario, container B has twice the volume of container A and thus twice the number of molecules, resulting in a total internal energy that is also twice that of container A. Therefore, the correct answer is (a).
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eprparadox
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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



[tex] U = \frac{1}{2}Nfk_BT [/tex]

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?
 
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  • #2
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.
 
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Hey, awesome thanks so much I like Serena!
 

1. What is the definition of internal energy of an ideal gas?

The internal energy of an ideal gas refers to the total energy of the gas, including both its kinetic energy (movement) and potential energy (interactions between molecules).

2. How does temperature affect the internal energy of an ideal gas?

According to the ideal gas law, the internal energy of an ideal gas is directly proportional to its temperature. This means that as the temperature increases, the internal energy of the gas also increases.

3. What is the mathematical equation for calculating the internal energy of an ideal gas as a function of temperature?

The equation for calculating the internal energy of an ideal gas is U = (3/2)RT, where U is the internal energy, R is the gas constant, and T is the temperature in Kelvin.

4. How does the internal energy of an ideal gas change when the volume or pressure is altered?

According to the first law of thermodynamics, the internal energy of an ideal gas remains constant when the volume or pressure is altered. This means that if the volume or pressure increases, the temperature will also increase to maintain the same internal energy.

5. Can the internal energy of an ideal gas ever be negative?

No, the internal energy of an ideal gas cannot be negative. This is because the internal energy is a measure of the total energy of the gas, and energy cannot be negative. However, the change in internal energy can be negative if the gas loses energy through work or heat.

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