Calculating the amount of heat lost/gained at constant pressure

[Shivani Sakthi 1l]

Hello! During lecture, we learned about the difference between Cv, or the molar heat capacity of gas at a constant volume, and Cp, or the molar heat capacity of gas at a constant pressure. I understand that when the pressure of a gas is kept constant, when temperature increases, the volume of the gas must change due to the Ideal Gas Law. This means that when the piston is moving to a new position to increase volume, work is being done. Therefore, work of expansion is done. However, this contrasts with Cv because when volume is kept constant, the piston cannot move even as temperature increases. This means that no work of expansion is done and energy is not being lost. Using this and the definition of molar heat capacity, we were able to construct the equation qp=nCp(deltaT) in order to find the amount of heat required under constant conditions. This relationship can also be delineated using the specific heat capacity, rather than molar heat capacity[b]. However, why are we unable to delineate this relationship when it comes to volume? In other words, why is it incorrect to have the equation qv=gCp(deltaT). Is this because when volume is constant, there is no change in volume and thus no work of expansion when temperature changes? If volume is constant, does pressure need to rise if T increases? Does that mean work is being done?

thank you for the clarification

[Mia Yamada 1J]

Hi Shivani!

I believe you are correct in terms of not being able to have the equation qV=gCv(deltaT), because no expansion work is being done when the volume is kept constant.

To answer your other questions...
Just as volume increases as pressure is kept constant when temperature increases, pressure increases as volume is kept constant when temperature increases. This relationship can be seen in the Ideal Gas Law, since the number of moles and the ideal gas constant are unchanging, as temperature increases pressure and volume as a whole must adjust along with it. So if volume is kept constant, then pressure must adjust, and vice versa.

So yes, if volume is constant, pressure needs to rise if T increases. However, no work is being done in this case, since the system is not being expanded. In other words, the piston is not moving. :)

[claire smith]

Additionally, q is referring to heat (essentially a measure of the movement of particles). Conversely, delta H refers to the net enthalpy change in a reaction. At a constant volume, pressure is changing, and therefore particle collisions also change. This makes sense as to why heat and delta H are not longer interchangeable. Hope that makes sense.