Question

What is heat capacity at constant volume and constant pressure what is the relation between them?

Answer 1

The heat capacity of a defined system is the amount of heat needed to raise the system's temperature by one degree. This is different when the heat is supplied under constant pressure and constant volume (no expansion) condition.

During constant volume, no expansion of the fluid occurs. But in constant pressure some amount of work is utilized for expansion process. At constant pressure, some of the energy you put in goes into raising the temperature (internal energy) and some of it goes into doing work by expanding the ideal gas.

This applies for compressible fluids ( gas) alone. Liquids and solids can be considered to be incompressible since the amount of work utilized for expansion is very very negligible.

For solids and liquids, Cp = Cv = C

No distinct heat capacity values at constant pressure and temperature.

What are Heat Capacity C, CP, and CV?

The molar heat capacity C, at constant pressure, is represented by CP.At constant volume, the molar heat capacity C is represented by CV.

In the following section, we will find how CP and CV are related, for anideal gas.

The relationship between CPand CV for an Ideal Gas

From the equation q = n C ∆T, we can say:

At constant pressure P, we have

qP = n CP∆T

This value is equal to the change in enthalpy, that is,

qP = n CP∆T = ∆H

Similarly, at constant volume V, we have

qV = n CV∆T

This value is equal to the change in internal energy, that is,

qV = n CV∆T = ∆U

We know that for one mole (n=1) of an ideal gas,

∆H = ∆U + ∆(pV ) = ∆U + ∆(RT) = ∆U + R ∆T

Therefore, ∆H = ∆U + R ∆T

Substituting the values of ∆H and ∆U from above in the former equation,

CP∆T = CV∆T + R ∆T
CP = CV + R
CP – CV = R

Answer 2

Answer:

During constant volume, no expansion of the fluid occurs. But in constant pressure some amount of work is utilized for expansion process.

At constant pressure, some of the energy you put in goes into raising the temperature (internal energy) and some of it goes into doing work by expanding the ideal gas.