By Team Aakash Byju's
How to Derive the Relationship Between
Cp and CV for an Ideal Gas?
An ‘ideal gas’ is a hypothetical gas that contains molecules that do not interact with each other and occupy negligible space.
The pressure (P), volume (V), and temperature (T) of an ideal gas are related by a law called ‘
Ideal Gas Law
’.
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Mathematically, the law can be written as:
What is Cp?
It is a measure of molar heat capacity at constant pressure.
What is Cv?
It is the measure of molar heat capacity at constant volume.
The amount of heat required to bring about a ∆T difference in temperature of one mole of any matter is given by the formula:
The same formula at constant pressure and constant volume can be written as:
For 1 mole of an ideal gas, we know that:
Now, substitute the value of
∆H
and
∆U
in the above equation, we get:
The above equation is the relationship between
CP
and
CV
for an ideal gas.
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