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

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In summary, Mayer's equation (1) states that the difference between specific heat at constant pressure and specific heat at constant volume is equal to the universal gas constant. However, equation (2) uses a different form of the equation, where the units of C(p) and C(v) are in gram molecular specific heat and R is divided by J, the mechanical equivalent of heat. This changes the unit of R from a work unit to a heat unit.
  • #1
Amith2006
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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)?
 
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  • #2
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.
 
  • #3
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?
 

1. What do the units Joule/Kilogram-Kelvin represent in equation (1)?

The units Joule/Kilogram-Kelvin in equation (1) represent the specific heat capacity of a substance. It is a measure of the amount of energy required to raise the temperature of one kilogram of the substance by one Kelvin.

2. Why are the units of C(p) and C(v) in equation (1) given in Joule/Kilogram-Kelvin?

The units of Joule/Kilogram-Kelvin are commonly used for specific heat capacity because they are derived from the fundamental units of energy, mass, and temperature. This makes them a more universal measurement that can be easily converted to other units if needed.

3. Can the units of C(p) and C(v) in equation (1) be converted to other units?

Yes, the units of Joule/Kilogram-Kelvin can be converted to other units such as Joule/Gram-Kelvin or Calorie/Gram-Celsius. This can be done by using conversion factors or equations derived from the specific heat capacities of water.

4. What is the difference between C(p) and C(v) in equation (1)?

C(p) and C(v) refer to the specific heat capacities at constant pressure and constant volume, respectively. C(p) takes into account the heat required to raise the temperature of a substance while also allowing for expansion, whereas C(v) only considers the energy needed to increase the temperature at a constant volume.

5. How are the units of C(p) and C(v) in equation (1) related to the properties of a substance?

The units of C(p) and C(v) are related to the molecular structure and composition of a substance. Different substances have different specific heat capacities due to factors such as the number of atoms in a molecule, bond strength, and intermolecular forces. This allows scientists to use specific heat capacity as a way to identify and study different substances.

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