C_v vs. C_p

[Ysabelle Magat 1E]

Can someone explain why C_v is lower than C_p? I know from the equation pV= nrT that by increasing temperature at constant pressure work is being done as the piston moves up and changes volume, but I'm unsure why more heat is required for constant pressure vs. constant volume.

[Vivek Chotai 2C]

Since work is being done, some of the energy from the heat is used up. So there would be less energy left to actually heat up the substance and change its temperature. You can think of it as even though you add energy and heat up the calorimeter, some of the energy leaks and is used to do work instead of focusing all to change the temperature.

[Rhea Desai 1A]

As a gas heats up, the pressure increases. In order to maintain constant pressure, we increase the volume. This means that energy is used to move the piston up and increase the volume. Since some energy is being used to do work and move the piston, it takes more energy to raise the temperature by 1 degree C, so Cp is higher than Cv.

[Kaira Shibata 1E]

Energy must be used the move the piston up. That takes up more energy that for the constant volume calorimeter in which case there is nothing doing work.

[Erika Li 1E]

Gases expand much more than solids or liquids when they are heated. This means that if you heat a gas at constant pressure, the volume must increase by moving the piston up in order to maintain constant pressure. At constant pressure, not all of the heat supplied is used to raise the temperature and some of it is used to do work in moving the piston up. In contrast, at constant volume, all the energy is used to increase the temperature of the system. Given that C=q/T, more heat must be supplied to raise the temperature by 1 C at constant pressure, so Cp is higher than Cv.

[205678283]

In lecture today he was saying that Cv is lower than Cp because when the pressure is constant, expansion work is being done, as the gas molecules push up on the piston to increase the volume, in order to compensate for the increase in temperature. Work is needed to push air out of the way at 1 atm. But when volume is constant, there is no energy lost from expansion work because the gas is not expanding -- the volume doesn't change.

[Grant_2A]

It takes energy to move the piston up and keep the constant pressure, this leaves the system with less energy to heat up one degree, so it requires more energy to do both things, whereas the constant volume scenario doesn't have to deal with this.

[Matthew Vu 3C]

C_p is greater because it also involves the work done, whereas C_v doesn't.

[205484435]

Cp is greater because it also takes into account that amount of heat used to do work

[Jack Amos 2I]

Just a follow-up question, how significant is the energy difference between a system with constant pressure and a system with constant volume?