# Why does the internal energy increase when a gas is compressed, despite there being a decrease in potential energy?

For a non-ideal gas,

When the gas is compressed, the potential energy of its molecules decreases. Doesn’t it?

Internal energy is the sum of kinetic and potential energies of the molecules.

Considering that, I don’t see why the internal energy increases. Is it because the increase in kinetic energy exceeds the decrease in potential energy?

*There is no heat exchange with the surroundings.

• In your last sentence did you mean to say decrease in potential energy and not increase? Otherwise it contradicts the first sentence. Jun 14, 2020 at 13:24
• Yes. You’re correct. I’ve edited it now. Jun 14, 2020 at 13:33
• We need some clarification. Are you saying there is in fact an increase in internal energy or are you asking if there is an increase in internal energy. Please clarify. Jun 14, 2020 at 13:52
• And also, just to be clear, you are not talking about an ideal gas. There is no change in potential energy of an ideal lgas. Jun 14, 2020 at 13:53
• The compression work translates to an increase in internal energy. The temperature (and KE) increases. However, in a non ideal gas, the PE decreases, no? Since change in internal energy is the sum of change in KE and PE, does it mean that the increase in KE exceeds the decrease in PE? Jun 14, 2020 at 13:56

Considering that, I don’t see why the internal energy increases. Is it because the increase in kinetic energy exceeds the decrease in potential energy?

You haven't specified the details of the process, but if in fact the internal energy increases as a result of the compression while the internal potential energy decreases, then yes the increase in kinetic energy must exceed the decrease in internal potential energy to satisfy conservation of energy (change in internal energy = change in internal kinetic energy + change in internal potential energy).

UPDATE

In view of your recent edits, namely that there is no heat exchange with the surroundings and the gas is non-ideal, then there will be an increase in internal energy. For that to be the case, the increase in internal kinetic energy due to the compression must exceed the decrease in internal potential energy in order for there to be an increase in internal energy. So my answer still applies.

Hope this helps.

• Well, internal energy is conserved, but where does compression work go? Doesn't compression work add to the system? I mean you should also consider compression work to truly satisfy conservation of energy. Jun 14, 2020 at 13:44
• @HarishChandraRajpoot Read my answer carefully. I said IF in fact there is an increase in internal energy and a decrease in potential energy, there must be an increase in kinetic energy, regardless of the process. I think we need clarification from OP. Jun 14, 2020 at 13:50
• Yes, you are right. But OP clearly says that gas is compressed this means that work is definitely done on the system so we can't ignore compression work to explain increase in internal energy of gas because compression work also makes. OP is also confused what actually he wants to ask. Jun 14, 2020 at 13:54

When a real (non-ideal) gas is compressed the intermolecular distances between gas molecules decrease. As a result the internal potential energy of the real gas decreases i.e. internal P.E. becomes more negative due to increase in forces of intermolecular attraction.

As there is no heat exchange with the surroundings hence the work done to compress the gas increases the internal kinetic energy as a result the temperature of gas also increases.

The increase in internal K.E. energy is more than the decrease in internal P.E.. Therefore there in increase in the internal energy of a real gas when compressed adiabatically.