Does hot air require more work to compress than cold air?

[Nabo00o]

Okey, simple question. As written in the title, I'm really not sure how this should work.
Should hot air need more energy to compress than cold air, is it the other way around or is there no difference?

This is asked because I need to find out if a physical system could work or not...
Any help appreciated!

Naboo

[Mapes]

Hi Nabo00o, welcome to PF. One way to tackle this is to assume ideality (i.e., PV=nRT) and calculate the work needed to compress the gas, \int -P\,dV. Does this help?

[Q_Goest]

Yes, the warmer the gas, the more power needed to compress given any pressure inlet and outlet and flow rate.

[Nabo00o]

@Mapes
Thank you Mapes.
Yes I think that will help me as soon as I understand the formula correctly.

@Q_Goest
Okey. But is this only because air closer to total zero is harder to expand, or is it more or less proportional with the change of temperature?
Sorry if this is a dumb question, I just need to understand it correctly.