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### Course: Class 11 Physics (India)>Unit 17

Lesson 2: Kinetic molecular theory of gases

# Heat capacity at constant volume and pressure

Explore the kinetic energy of a monatomic ideal gas and how it changes with heat and work. Uncover the first law of thermodynamics and its implications on internal energy. Dive into the concept of heat capacities at constant volume and pressure, and their relationship with the Ideal Gas Law. Created by David SantoPietro.

## Want to join the conversation?

• Where did you derive Uint= 3/2PV=3/2NKT=3/2nRT?
• Videos are in the wrong order. Kinetic molecular theory of gases.
• At , it was said Pressure remained constant even the piston moved up due to addition of heat. What about in case of work being done on the gas by applying external force (piston moving down) , meaning would pressure still remains constant while work is being done on the system and in addition there is a supply of heat from the bottom?? Not sure we need to add heat at all in this case?? so confused ...Please help
• U is given to be as 3/2 PV or 3/2nRT.....but at it is given that ∆U =3/2PV =nR∆T. Ok let us say for once that they might have forgotten to put the ∆V(in PV) sign over there however the process was being defined for constant volume therefore ∆V =0 so ∆U should also be zero
• Will we ever need to know this on MCAT?
• Does a monatomic gas have lower or higher heat capacity than a diatomic, or polyatomic?
• Lower. Molar heat capacity at constant pressure = (f+2)/2 and molar heat capacity at constant volume = f/2.

Where f is the number of degrees of freedom. For a monoatomic gas, f =3 and for a diatomic gas we generally consider f=5.
(1 vote)
• So does it mean that at constant pressure more heat is required to increase the temperature than whats required at constant volume?
(1 vote)
• yes, because at constant pressure some of the energy from the heat transfer will be use to move the piston up (do work)
• hello, for an approximation of heating up the air of an office would we use Cp or Cv?
(1 vote)
• In my opinion, its gonna be Cv since the volume of the office will remain constant.
• how would you figure out the heat capacity of a liquid or solid or a realistic(instead of ideal) gas?
• Then many external factors come into play, which are well beyond the scope of the video. :)
Also, watch the the beginning minutes of the next video in the series (Kinetic Molecular Theory of gases). It list the necessary assumptions for an ideal gas. Peace :)
• If I increase the number of moles of gas because of a chemical reaction, but keep volume constant and I increase the temperature is the work done still 0?
(1 vote)
• Since the volume does not change, the work done by the gas is still zero.
(1 vote)
• When we measure specific heat at constant volume,pressure is changing. We know that specific heat depends on pressure.Therefore does specific heat also changes?
(1 vote)