Isothermal and Adiabatic Processes — Formula Sheet

Boyle's Law: PV = constant

Poisson's Law: PV^γ = constant

Adiabatic T-V relation: TV^(γ-1) = constant

Adiabatic T-P relation: T^γ / P^(γ-1) = constant

Slope of isothermal curve: (dP/dV)_iso = -P/V

Isothermal Work Done: W = μRT loge(V2/V1) = μRT loge(P1/P2) = 2.3026 μRT log10(V2/V1) = 2.3026 μRT log10(P1/P2)

Adiabatic Work Done (P-V form): W = (1/(γ-1))(P1V1 - P2V2)

Adiabatic Work Done (T form, μ moles): W = (μR/(γ-1))(T1 - T2)

Adiabatic Work Done (T form, 1 mole): W = (R/(γ-1))(T1 - T2)

Cv = M·cv

Cp = M·cp

Mayer's Relation: Cp - Cv = R

For an ideal gas, an adiabatic process obeys Poisson's law

PV^γ = constant.

Temperature remains constant

ΔT = 0

Internal energy remains constant for an ideal gas

ΔU = 0

No heat exchange

ΔQ = 0

Poisson's law

PV^gamma = constant

Work formula

W = muRT loge(V2/V1)

Its slope is (dP/dV)_iso = -P/V.

Its slope is (dP/dV)_adia = -γP/V.

γ = Cp/Cv, where Cp and Cv are the molar specific heats at constant pressure and constant volume. γ is always greater than 1.