# Internal energy of ideal gas

• dlthompson81
In summary, the conversation discussed finding the total internal energy of a gas using the ideal gas law formula PV=nRT. After some confusion on which variable represented internal energy, the correct formula was identified as 3/2nRT. Using this formula, the total internal energy was calculated to be 5185.759887 J. The origin of this formula was not fully understood and the student recommended consulting their textbook for more information.

## Homework Statement

A container of volume 0.72 m^3 contains 1.4 mol of argon gas at 24 degrees C.

Assuming argon behaves as an ideal gas, find the total internal energy of this gas. The value of gas constant is 8.31451 J/mol x K.

PV=nRT

## The Attempt at a Solution

I'm not sure if that's the right formula or not. I don't know which letter would equal the internal energy. Am I missing a formula somewhere?

My teacher isn't going to be here next week, so I'm kind of stuck learning this on my own. I don't have too much of an understanding of it at all. Thanks for the help.

Ok, I found the formula 3/2nRT.

I got 5185.759887 J, and it was right.

I'm not quite sure where this formula came from. Can anyone explain that?

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I can't remember it off the top of my head. Isn't the formula derived in your textbook?

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

The internal energy of an ideal gas refers to the total energy that the gas molecules possess due to their motion and interactions with each other. It includes both the kinetic energy of the molecules' random motion and the potential energy of their interactions.

## 2. How is the internal energy of an ideal gas related to temperature?

The internal energy of an ideal gas is directly proportional to its temperature. This means that as the temperature of an ideal gas increases, so does its internal energy. This relationship is known as the equipartition theorem.

## 3. Does the internal energy of an ideal gas change during a change in volume or pressure?

Yes, the internal energy of an ideal gas can change during a change in volume or pressure. This is because the internal energy is dependent on the temperature, and changes in volume or pressure can lead to changes in temperature.

## 4. How is the internal energy of an ideal gas affected by the number of molecules?

The internal energy of an ideal gas is directly proportional to the number of molecules present. This means that as the number of molecules increases, so does the internal energy.

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

No, the internal energy of an ideal gas can never be zero as long as the gas is above absolute zero temperature. This is because the gas molecules will always have some amount of kinetic energy due to their random motion.