# Internal Energy of 1 mole of Ideal Gas

1. Dec 6, 2015

### Symara Cyr

1. The problem statement, all variables and given/known data
One litre cylinder contains 1 mole of the ideal gas molecules having the average kinetic energy of 0.1eV. What is the total energy of this gas?

2. Relevant equations
W = K + U

3. The attempt at a solution
I figured because the cylinder is closed, no stated temperature change, or volume/pressure change, there is no work? So U=-K
K = 0.1eV = 1.6 x10-20J.
Therefore, U = -1.6x10-20 J.

Is this line of thinking correct? Can it really be that simple..

2. Dec 6, 2015

### TSny

Welcome to PF!

You are given the average kinetic energy of a single molecule. You are asked for the total energy of all of the molecules in the cylinder.

3. Dec 6, 2015

### Mister T

Is that supposed to be $W=\Delta K +\Delta U$? In other words work equals change in energy?

Regardless, your reasoning is correct in that there is no work done and no change in energy, temperature, volume or pressure. But the question is not asking about how much the energy changes. It's asking what the energy is.

The energy of an ideal gas is the sum of the kinetic energies of the gas molecules.

4. Dec 6, 2015

### Symara Cyr

So, U = -1.6x10-20 J is for a single molecule. I adjust for the rest of the molecules by multiplying my number by Avogadro's number?

and yes, that's the equation I actually meant. My apologies!

5. Dec 6, 2015

### Staff: Mentor

For an ideal gas, the internal energy is equal to the sum of the kinetic energies of all the molecules comprising the gas. Since kinetic energy is positive definite, the internal energy cannot be negative.

Chet

6. Dec 6, 2015

### Mister T

Yes. it's a simple exercise, not really a problem.

You should be aware that the relation $W=\Delta K + \Delta U$ is valid only for particle-like objects, that is, objects that cannot possess internal energy.

The more general relation is the First Law of Thermodynamics. In thermodynamics you typically treat a collection of particles, a gas for example, which does possess internal energy.

7. Dec 7, 2015

### Symara Cyr

Awesome, okay. Thank you everyone so much!