# Cp and Cv Relationship for an Ideal Gas

When precise values are not needed or available, the following values can be used near room temperature:
Monatomic Gases (ex. Ar)
Diatomic Gases (ex. O2)
The definition of enthalpy is:
For ideal gases , this simplifies to:
The differential form of this equation is:
But, we showed on the previous two pages that:
Therefore:
Dividing each term by dT yields:
Roll your mouse over this box to close.
• Homework problem hints and answers
• Get Help from Dr. B in the LT Blog
• 120 day membership

Get it ALL for \$5 US

### Ch3, Lesson C, Page 7 - Cp and Cv Relationship for an Ideal Gas

• We begin with the definition of enthalpy because it provides us with the connection between enthalpy and internal energy.
• We then use the ideal gas EOS to replace P V-wiggle with RT.
• This is cool because now each term is a function of T only !
• Now, we can write the differential form of this equation and we can see some connections to the last two pages.
• We just learned that dU-wiggle is Cv dT and dH-wiggle is Cp dT.
• We can plug these two equations in for dU-wiggle and dH-wiggle and things start to simplify.
• The cool step is dividing thru by dT.  We no longer have a differential equation.
• What we have is a nice simple relationship between Cp and Cv.
• Just keep 3 things in mind:
• Cp is bigger than Cv
• This equation ONLY applies for ideal gases
• And to get a similar equation in terms of specific heats, all we need to do is divide by the molecular weight.  Just be careful with the units !
• So, all we need to do is look up the polynomial expression for Cp and the use this simple equation and, voila, we have Cv as well.
• If you are doing rough calculations or you cannot locate the Cp of the ideal gas you are working with, you can use the approximate values shown here.
• These only apply for monatomic and diatomic gases, but they just might come in handy !
• That wraps up our discussion of ideal gases, now let’s take a look at two other special types of materials: liquids and solids in which V-wiggle is a constant.