Cp vs Cv

[Vicky Tong 3E]

During lecture, Dr. Lavelle went over two diagrams for Cp and Cv. I believe he said that it was important to understand that Cp will do more work due to expansion. I'm not entirely sure if I understood this concept, so I would appreciate it if someone explained these diagrams!

[Mikayla 2G]

In order to keep a constant pressure, the volume of the container needs to be changed. Dr. Lavelle modeled a container that could expand as the temperature increased. In order to increase the volume, work needs to be done to make the container expand. So instead of all the energy going into the gas, some energy is used to move the container the gas is in, so the molar heat capacity of larger because it takes more energy to heat one mole of gas under constant pressure when part of the energy is being used to move the container.

Compared to under constant volume, there is no work being done on moving the container, so all the energy stays with the gas, meaning less energy has to be put in to increase the temperature of the gas and therefore the molar heat capacity is smaller.

[Arjan G 2H]

Hi! When looking at CP, the equation PV=nRT shows us that the pressure and temperature are the values that must stay constant, meaning the volume has to change. Cp itself represents the heat capacity of a gas at a constant pressure. In order to keep pressure constant when energy is being added into a system, we would need to expand the volume of the system. Expanding the volume can only be done by work, which means more energy is needed in Cp calculations. For Cv, which represents heat capacity at a constant volume, the volume is a fixed amount, and the pressure has a certain limit it can reach. This means that there is not that much work needed to be done on the system, as there is no expansion in volume. I hope this helped!

[Michael Vigman 2D]

The reason that two different molar specific heat capacities will be given (Cp & Cv) are for two different kinds of constant conditions: constant pressure vs. constant volume. At constant pressure, if heat is added, volume must increase in order to accommodate the increase in thermal energy such that the pressure can stay the same. If the volume is increasing, that means the system is doing work on its environment in order to expand.

However, at constant volume, if heat is added, since the volume is unable to increase then the pressure increases. In this case though, no work is being done since the gas is not moving any of its surroundings but rather the pressure is increasing.

I find it is simplest to think of these parameters microscopically. At constant volume, increased energy to the particles forces them to increase pressure which by definition is the collisions between the particles and their surroundings. At constant pressure, since the number/force of those collisions must stay constant (since pressure isn't changing), then they must be given more volume to spread out and use that added thermal energy.

[Hailey Sarmiento 3E]

Cp represents the molar heat capacity of a gas at a constant pressure. In order for a gas in a closed system to maintain constant pressure when heated, the piston must move to increase volume. Cv represents the molar heat capacity of a gas at constant volume, meaning the piston does not move when the system is heated so there is no volume expansion work.