# B Relation between pressure and volume when heating a gas

1. Jan 3, 2018

### ElectricRay

Hi all,

A happy 2018 for all PF members.

I have a question. Im trying to understand some basic principle of thermodynamics. My book tells me tge following:

"Heating of a gas at a constant pressure uses more heat as when heating the same gas a constant volume"

How do i interpret this? I find this paradoxical. If I visualize this for myself I come at the following:

I have a gas this gas is e.g. in a box which I will heat up to e certain temperature. Let say it gets 10 deg C higher. If the pressure is maintained constant (which i dont understand first of all, i thought that the pressure would increase as I heat the gas) I need more energie (joules) as when I heat up the gas to the same 10 deg C high but with a constant volume.

This all confuses me a lot. Can anybody help me understand this phenomena?

Raymond

2. Jan 3, 2018

### jbriggs444

If pressure is maintained constant then volume must be increasing. For instance, you are heating a gas in a cylinder with a piston at one end. The heated gas did mechanical work to move the piston against a [nearly] equal resistance. That takes energy.

3. Jan 3, 2018

### phyzguy

We always have PV = nkT. If the volume is held constant, then the pressure will increase as the temperature is increased. In order to hold the pressure constant, the volume must be allowed to increase as the temperature increases. We could do this, for example, by having a chamber with a piston held in place with a constant force, like a weight pushing down on it. Then as the temperature increases, the piston will move up, keeping the pressure constant and allowing the volume to increase. In this case, the gas will do work on the moving piston, so you have to put in more energy than in the case where the volume stays constant.

4. Jan 3, 2018

### ElectricRay

Clear that feels intuitively but now when volume is maintained constant. So we block the piston as in your example. In that case the pressure will increase, right?

But why the amount of energy needed when one maintains pressure constant is more as when we keep the volume constant, hence delta T is the same in both cases.

5. Jan 3, 2018

### ElectricRay

Ahhhh ok yes this makes sense. Thanks guys I appreciate the help so fast.