Heat Capacity

[CarolYassa2K]

What is the difference between molar heat capacity of a gas at constant volume and molar heat capacity of a gas at constant pressure? Aren't volume and pressure directly related?

[MaxReines1A]

I'm not entirely sure, but I imagine that it has something to do with work. At a constant volume, a gas cannot expand when heated, so it cannot offload any of its excess energy through work. However, at a constant pressure, such as inside a piston, the gas does expand. Since work = force * distance, this expansion is a form of work, and will require some amount of energy. Therefore, the molar heat capacity at constant pressure should be higher than the molar heat capacity at constant volume; the gas can absorb more heat because it releases some as work.

[Marina Nimnual]

Typically, the Molar Heat Capacity of a gas at constant pressure is higher than the Molar Heat Capacity of a gas at constant volume. This is because the energy required to heat up 1 mole at constant volume will focus only on heating the molecules. However, the the energy required to heat up 1 mole at constant pressure needs energy to heat up the molecules AND move the piston up, which means that more energy is needed to do work.

[Allie Kinsey 3H]

Sometimes the volume and pressure are not directly related, based on the reaction/production of products (I think).

[OhSun Kang 1G]

You're right! Pressure and volume are inversely related (Boyle's Law). However, that is only if you are letting both of them behave as variables. If you hold one of them constant, then Boyle's Law no longer holds. This is why we must distinguish between constant volume and constant pressure.

Also, when the volume is constant, pretty much all the heat energy transferred to the gas mixture goes toward increasing the temp of the gas. However, when pressure is constant, the system will expand to keep pressure from increasing (if you look at the Ideal/Combined Gas Law, the only way to keep pressure constant when temp is increasing is to increase the volume). As you can imagine though, if there's an external pressure (like air), the system will lose some energy pushing against it during expansion (we call this DOING work). As a result, for the same temperature increase, you'll have to add more heat to a system with constant pressure than constant volume.