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SECOND LAW OF THERMODYNAMICS. Heat engine. HEAT ENGINE, HEAT PUMP, REFRIGERATOR. Source & sink. Entropy increase principle. Clausius Inequality: For internally reversible cycles:. Entropy. S gen > 0 irreversible processes = 0 reversible processes < 0 impossible processes.
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Clausius Inequality: • For internally reversible cycles:
Entropy • Sgen > 0 irreversible processes = 0 reversible processes < 0 impossible processes
Isentropic Processes • Isentropic process; internally reversible, adiabatic, entropy remains constant Δs = 0 or s2 = s1
Entropy • Essentially Isentropic Processes • Pumps • Turbines • Nozzles • Diffusers
Property Diagrams • Temperature-entropy (T-s) diagrams • Area under process curve on a T-s diagram equals heat transfer during an internally reversible process
Property Diagrams • Isentropic processes are a vertical line on T-s diagrams
Entropy • Entropy is: measure of molecular disorder, molecular randomness
Entropy • Boltzmann equation: S = k ln(p) where k =1.3806*10-23 J/K p = thermodynamic probability, number of possible microscopic states of system
Third Law of Thermodynamics • The entropy of a pure crystalline substance at absolute zero temperature is zero, since there is no uncertainty about the state of the molecules at that instant • Provides an absolute reference point for determining entropy
Entropy • Work changed to heat increases entropy
Entropy • During heat transfer net entropy increases
Entropy • To find the change in entropy, need to do the cycle integral of δQ/T. • If isothermal, only need the function for Q • If not isothermal, need functions for Q and T
Entropy • Can find entropy by integration of either equation • Need to know the relationship between du or dh and temperature • For ideal gases • du = cv dT • Or dh = cp dT • And Pv=RT
Entropy Changes of Liquids and Solids • Liquids and solids are incompressible • dv = 0 • Also cv= cp=c and du= c dT
Entropy Change of Ideal Gases • In the basic equation, substituting du = cv dT and P = RT/v • Substituting dh = c dT and v = RT/P
Entropy Change of Ideal Gases • Need the relationship between the specific heats and temperature • Assume constant specific heats, simpler integration, approximate analysis • Work with variable specific heats, use tables, exact analysis
Variable Specific Heats (Exact Analysis) • If temperature change is large • Specific heats are non-linear with temperature • Need accurate relationships • Calculate integrals with respect to reference entropy (at absolute zero)
Variable Specific Heats (Exact Analysis) • So we can find • And substituting into • Get