fundamentals of engineering supplied-reference handbook - Ventech!

SECOND LAW OF THERMODYNAMICS
Thermal Energy Reservoirs
∆Sreservoir = Q/Treservoir , where
Q is measured with respect to the reservoir.
Kelvin-Planck Statement of Second Law
No heat engine can operate in a cycle while transferring heat
with a single heat reservoir.
COROLLARY to Kelvin-Planck: No heat engine can have a
higher efficiency than a Carnot cycle operating between the
same reservoirs.
Clausius' Statement of Second Law
No refrigeration or heat pump cycle can operate without a
net work input.
COROLLARY: No refrigerator or heat pump can have a
higher COP than a Carnot cycle refrigerator or heat pump.
VAPOR-LIQUID MIXTURES
Henry's Law at Constant Temperature
At equilibrium, the partial pressure of a gas is proportional
to its concentration in a liquid. Henry's Law is valid for low
concentrations; i.e., x ≈ 0.
pi = pyi = hxi, where
h = Henry's Law constant,
pi = partial pressure of a gas in contact with a liquid,
xi = mol fraction of the gas in the liquid,
yi = mol fraction of the gas in the vapor, and
p = total pressure.
Raoult's Law for Vapor-Liquid Equilibrium
Valid for concentrations near 1; i.e., xi ≈ 1.
pi = xi pi * , where
pi = partial pressure of component i,
xi = mol fraction of component i in the liquid, and
pi * = vapor pressure of pure component i at the
temperature of the mixture.
ENTROPY
ds = (1/T) δQrev
( )
2
2 1 1 1/ − = ∫ δ rev
s s T Q
Inequality of Clausius
∫ (1/ T ) δQ
≤ 0
2
1
∫
( )
rev
1/T δQ≤ s −s
2 1
Isothermal, Reversible Process
∆s = s2 – s1 = Q/T
60
Isentropic Process
∆s = 0; ds = 0
A reversible adiabatic process is isentropic.
Adiabatic Process
δQ = 0; ∆s ≥ 0
Increase of Entropy Principle
∆stotal
= ∆ssystem
+ ∆ssurroundings
≥ 0
∆s�
total = ∑m�outsout − ∑m�insin
− ∑ Q�
T ≥
THERMODYNAMICS (continued)
( )
external
external
Temperature-Entropy (T-s) Diagram
Q rev
= ∫
2
T ds
1
Entropy Change for Solids and Liquids
ds = c (dT/T)
s2 – s1 = ∫ c (dT/T) = cmeanln (T2 /T1),
where c equals the heat capacity of the solid or liquid.
Irreversibility
I = wrev – wactual
EXERGY
Exergy is the portion of total energy available to do work.
Closed-System Availability
(no chemical reactions)
φ = (u – uo) – To (s – so) + po (v – vo)
where the subscript "o" designates environmental conditions
wreversible = φ1 – φ2
Open-System Availability
ψ = (h – ho) – To (s – so) + V 2 /2 + gz
wreversible = ψ1 – ψ2
Gibbs Free Energy, ∆G
Energy released or absorbed in a reaction occurring
reversibly at constant pressure and temperature.
Helmholtz Free Energy, ∆A
Energy released or absorbed in a reaction occurring
reversibly at constant volume and temperature.
0