# Ws, Non-Isothermal Processes, Ideal Gas

( δ ≠ 1 )
For

, we can use the

#### ideal gas EOS

to simplify this equation.
Useful equations for polytropic processes for ideal gases from Lesson 7E.

,

,

,

#### polytropic

processes with ΔEpot = 0 and ΔEkin = 0
• δ ≠ 1
• #### Ideal gas

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### Ch 8, Lesson B, Page 14 - Ws, Non-Isothermal Processes, Ideal Gas

• For ideal gases, we can use the ideal gas equation of state to replace P Vhat with R T over the molecular weight.
• We can do this for both P1 V1,hat and P2 V2,hat.
• The result is the even simpler equation in the yellow box.
• This equation is very useful, especially in combination with these two relationships among P, V and T that we derived in lesson 7E for polytropic processes.
• Keep in mind all of the assumptions that we made in the derivation of the equation in the yellow box, especially that it applies only to ideal gases.
• Now, let’s consider polytropic processes in which δ = γ, the heat capacity ratio.