IIT JEE Physics Formula Revision 27. Specific Heat of Capacities of Gases

1. Specific heat capacity of a substance s

s = ΔQ/mΔT

2. Specific heat capacity of a substance at constant volume is denoted by symbol sv

sv = [ΔQ/mΔT] heat given at constant volume

3. Specific heat capacity of a substance at constant pressure is denoted by symbol sp

sp = [ΔQ/mΔT] heat given at constant pressure

4. Molar heat capacity of a substance at constant volume is denoted by symbol Cv

Cv = [ΔQ/nΔT] heat given at constant volume

5. Molar heat capacity of a substance at constant pressure is denoted by symbol Cp

Cp = [ΔQ/mΔT] heat given at constant pressure

6. Relation between Cp and Cv for an ideal gas

Cp - Cv = R
or
Cp = Cv + R

7. Cv = i/n (dU/dT)
dU = n(Cv)dT
8. Taking energy to be zero at t = 0
U = n(Cv)T

9. pV^γ = constant

γ = Cp/Cv

10. In a reversible adiabatic process

T^γ/p^γ-1 = constant

11. In a reversible adiabatic process

TV^γ-1 = constant

12. Work done in an adiabatic process

W = (p1V1 - p2V2)/(γ-1)

For monoatomic gas

U = n (3/2) RT

Cv = 3/2R

Cp = 5/2R

γ = 5/3 = 1.67


For diatomic gas without vibration


Cv = 5/2R

Cp = 7/2R

γ = 7/5 = 1.40

If the molecules vibrate

Cv = 7/2R

Cp = 9/2R

γ = 9/7 = 1.29