Formulas for Molar Heat Capacity at Constant Pressure/Volume

In summary, the textbook states that for constant volume, Q = nCvdT and for constant pressure, Q = nCpdT. However, a TA mentioned that for constant volume, dU = nCvdT and for constant pressure, dU = nCpdT. This may be confusing, but both equations can be correct depending on the context. At constant volume, the work is 0 so dQ = dU = nCvdT, while at constant pressure, the gas does work and more heat is needed to raise its temperature, so dQ = dU + PdV = nCpdT. Ultimately, Cp = Cv + R for an ideal gas.
  • #1
mneox
36
0

Homework Statement



Just wanted to find some clarity regarding this subject. In my textbook, it states that Q = nCvdT for constant volume and Q = nCpdT for constant pressure.

However, one of the TA's in my classes were telling us how dU = nCpdT for constant pressure and dU = nCvdT for constant volume.

Which is right? I'm majorly confused right now.

Homework Equations



dQ = dU + dW

The Attempt at a Solution



No solution really needed, I just want some clarification as to which is right. I know that for constant volume processes, the work will be 0 and therefore dQ = dU which would mean they can BOTH equal nCvdT?

But what about nCpdT? That's what I'm confused about. Thanks for any help!
 
Physics news on Phys.org
  • #2
The internal energy of the gas increases by adding heat Q to it and/or doing positive work W on it: dU=Q+W. At constant volume, the work is zero, so Q=dU =n Cv dT. At constant pressure, the gas does work of PdV while taking heat on, so more heat is needed to rise its temperature. Cp is the heat which rises the temperature of 1mol gas by 1 K. At constant pressure dU=Q-PdV=nCp dT-PdV. As PV=nRT, dU=nCpdT-nRdT=n dT(Cp-R). But dU=n Cv dT, so Cp=Cv+R for an ideal gas.

ehild
 

1. What is the difference between molar heat capacity at constant pressure and constant volume?

Molar heat capacity at constant pressure refers to the amount of heat needed to raise the temperature of one mole of a substance by one degree Celsius while maintaining constant pressure. Molar heat capacity at constant volume, on the other hand, refers to the amount of heat needed to raise the temperature of one mole of a substance by one degree Celsius while maintaining constant volume. The main difference between the two is that at constant pressure, the substance is allowed to expand and do work, while at constant volume, the substance is not allowed to do work.

2. How are molar heat capacities at constant pressure and volume related?

The molar heat capacities at constant pressure and volume are related by the specific heat capacity of the substance, which is a constant value for a given substance. The molar heat capacity at constant pressure is equal to the molar heat capacity at constant volume plus the gas constant (R).

3. What factors affect the molar heat capacity of a substance?

The molar heat capacity of a substance is affected by its molecular structure, mass, and intermolecular forces. Substances with more complex molecular structures tend to have higher molar heat capacities, as do substances with higher molecular masses. Intermolecular forces also play a role, as substances with stronger intermolecular forces require more energy to raise their temperature.

4. How is the molar heat capacity of a substance determined experimentally?

The molar heat capacity of a substance can be determined experimentally by measuring the temperature change of a known mass of the substance when a known amount of heat is added. This can be done at either constant pressure or constant volume, and the molar heat capacity can be calculated using the equations Cp = q/mΔT or Cv = q/mΔT, where Cp is the molar heat capacity at constant pressure, Cv is the molar heat capacity at constant volume, q is the amount of heat added, m is the mass of the substance, and ΔT is the change in temperature.

5. Can the molar heat capacity of a substance change?

Yes, the molar heat capacity of a substance can change depending on the conditions in which it is measured. For example, the molar heat capacity at constant pressure may be different from the molar heat capacity at constant volume, and both values may change with temperature and pressure. Additionally, the molar heat capacity of a substance can change with a phase change, as different amounts of energy are required to raise the temperature of a substance in different phases.

Similar threads

Thermodynamics problem: Heat capacity of a Gas
    • Introductory Physics Homework Help
Replies
11
Views
1K
Specific Heat Capacity Derivation
    • Introductory Physics Homework Help
Replies
4
Views
973
What is the molar heat capacity of an ideal gas at constant pressure and volume?
    • Introductory Physics Homework Help
Replies
5
Views
2K
Heat Capacity relations for 1st order phase transition
    • Introductory Physics Homework Help
Replies
1
Views
1K
I Cannot understand formula for molar heat capacities of an ideal gas
    • Thermodynamics
Replies
22
Views
2K
Heat capacity and temperature problem
    • Introductory Physics Homework Help
Replies
5
Views
760
Mixing two ideal gases with different V, T at constant pressure
    • Introductory Physics Homework Help
Replies
16
Views
2K
Entropy and the Helmholtz Free Energy of a Mass-Piston System
    • Introductory Physics Homework Help
Replies
8
Views
1K
Molar heat capacity at constant pressure/volume
    • Introductory Physics Homework Help
Replies
2
Views
2K
Molar Heat Capacity: Find Value of k
    • Introductory Physics Homework Help
Replies
8
Views
3K

Hot Threads

Recent Insights

Back
Top