What We Know by Definitions
Isothermal Case
By isothermal we mean that temperature is held constant. The following is true:
∆U = ∆H = 0
∆S = R * ln( V2/V1 ) = R * ln( P1/P2 ) (substitutions with ideal gas law)
q = w = RT * ln( V2/V1 ) = RT * ln( P1/P2 ) (substitutions with ideal gas law)
w = ∫ PdV
P1V1 = P2V2 (substitutions with ideal gas law)
Isobaric Case
By isobaric we mean that pressure is held constant. The following is true:
∆U = ∫ CvdT
∆H = ∫ CpdT
∆S = ∫ CpdT / T
q = ∆H
w = ∫ PdV
Isochoric Case
By isochoric we mean that volume is held constant. The following is true:
∆U = ∫ CvdT
∆H = ∫ CpdT
∆S = ∫ CvdT / T
q = ∆U
w = 0
Adiabatic Case
By adiabatic we mean that heat flow is held constant. This is also referred to as reversible adiabatic. The following is true
∆U = ∫ CvdT
∆H = ∫ CpdT
∆S = 0
q = 0
w = - ∆U
P1(V1^ɣ) = P2(V2^ɣ) ( ɣ is lowercase greek letter gamma)
ɣ = Cp/Cv = (R + Cv) / Cv
Let me know if you’d like further explanations on how any of these were derived! The next post will be an example(or more than one? I’m not sure yet) of how to use what we know to solve for different values of interest in a thermodynamic problem. Again, everything we have done thus far is with regard to ideal gases.
