Units of C(p) and C(v) in equation (1) are Joule/Kilogram-Kelvin.

[Amith2006]

Homework Statement

1) According to Mayer’s equation,
C(p) – C(v) = R ------------ (1)
Where C(p) = specific heat at constant pressure
C(v) = specific heat at constant volume
R = Universal gas constant
But sometimes the above equation is used in the following way,
C(p) – C(v) = R/J ---------------- (2)
Where C(p) = gram molecular specific heat of the gas at constant pressure
C(v) = gram molecular specific heat of the gas at constant volume
R = Universal gas constant
J = Mechanical equivalent of heat

Homework Equations

The Attempt at a Solution

What are the units of C(p) & C(v) in equation(1)?

 

[tandoorichicken]

because the units on the two sides of the equation must match in order for the equation to be valid, the units of C_p and C_v must be the same as the units for the universal gas constant R.

 

[Amith2006]

If we divide R by J then the unit of R will be Calorie/mole.Kelvin. So by doing this we change the unit of R from work unit to heat unit, isn't it?