Formulas Flashcards
differential form of the first law
dU = δQ + δW
all infinitesimal changes
U - internal energy (J)
Q - heat or thermal energy (J)
W - work (J)
second law
ΔS ≥ 0
reciprocal theorem
(∂x/∂y)(z) = [(∂y/∂x)(z)]^-1
reciprocity theorem
(∂x/∂y)(z) (∂y/∂z)(x) (∂z/∂x)(y) = -1
work during reversible processes
δW = -PdV
W = -(2 ∫ 1) PdV
heat capacity at constant volume
C(V) =lim(ΔT->0) (∂Q/∂T)(V) = (∂U/∂T)(V)
enthalpy
H = U + PV
enthalpy in differential form
dH = d(U+PV) = dU +PdV + VdP = ∂Q + VdP
heat capacity at constant pressure
C(P) =lim(ΔT->0) (∂Q/∂T)(P) = (∂H/∂T)(P)
efficiency of an engine
η = 1 - Q(2)/Q(1)
efficiency of a carnot engine
η(C) = 1 - T(2)/T(1)
triple point of water
T(K) = 273.16K Q/[Q(TP) H(2)O]
efficiency of a carnot refrigirator
η(C)^(R) = T(2)/T(1)-T(2)
efficiency of a carnot heat pump
η(C)^(HP) = Q(1)/Q(1)-Q(2) = T(1)/T(1)-T(2)
Clausius inequality
∮ δQ/T(0) ≤ 0
central equation of thermodynamics
dU = TdS - pdV
δQ
= TdS
δW
= -PdV
entropy change for heating a body
ΔS = cmln(Tf/Ti)
entropy change for adding heat to a reservoir at constant T
ΔS = Q/T
entropy change for phase changes
phase changes are isothermal processes
ΔS = mL/T
absolute entropy of an ideal gas
ΔS = n[c(V) ln(T2/T1) + Rln(V2/V1)]