ENGR 2213 Thermodynamics F. C. Lai School of Aerospace and Mechanical Engineering University of Oklahoma

Increase-in-Entropy Principle (ΔS) adiabatic ≥ 0 A system plus its surroundings constitutes an adiabatic system, assuming both can be enclosed by a sufficiently large boundary across which there is no heat or mass transfer. (ΔS) total = (ΔS) system + (ΔS) surroundings ≥ 0 system surroundings

Increase-in-Entropy Principle S gen = (ΔS) total Causes of Entropy Change ► Heat Transfer Isentropic Process > 0irreversible processes = 0reversible processes < 0impossible processes ► Irreversibilities A process involves no heat transfer (adiabatic) and no Irreversibilities within the system (internally reversible).

Entropy Change of an Ideal Gas T ds = du + p dv For an ideal gas, du = c v dT, pv = RT

Entropy Change of an Ideal Gas T ds = dh - v dp For an ideal gas, dh = c p dT, pv = RT

Entropy Change of an Ideal Gas Reference state: 1 atm and 0 K Standard-State Entropy

Isentropic Processes of Ideal Gases 1. Constant Specific Heats (a) (b)

Isentropic Processes of Ideal Gases 1. Constant Specific Heats R = c p – c v k = c p /c v R/c v = k – 1 (a)

Isentropic Processes of Ideal Gases 1. Constant Specific Heats R = c p – c v k = c p /c v R/c p = (k – 1)/k (b)

Isentropic Processes of Ideal Gases 1. Constant Specific Heats Polytropic Processes pV n = constant n = 0 constant pressure isobaric processes n = 1 constant temperature isothermal processes n = k constant entropy isentropic processes n = ±∞ constant volume isometric processes p 1 V 1 k = p 2 V 2 k

Isentropic Processes of Ideal Gases 2. Variable Specific Heats Relative Pressure p r = exp[sº(T)/R] ► is not truly a pressure ► is a function of temperature

Isentropic Processes of Ideal Gases 2. Variable Specific Heats Relative Volume v r = RT/p r (T) ► is not truly a volume ► is a function of temperature

Work reversible work in closed systems reversible work associated with an internally reversible process an steady-flow device ► The larger the specific volume, the larger the reversible work produced or consumed by the steady-flow device.

Work To minimize the work input during a compression process ► Keep the specific volume of the working fluid as small as possible. To maximize the work output during an expansion process ► Keep the specific volume of the working fluid as large as possible.

Work Steam Power Plant ► Pump, which handles liquid water that has a small specific volume, requires less work. Gas Power Plant Why does a steam power plant usually have a better efficiency than a gas power plant? ► Compressor, which handles air that has a large specific volume, requires more work.

Ideal Rankine Cycles T S Process 1-2: isentropic compression in a pump Process 2-3: constant-pressure heat addition in a boiler Process 3-4: isentropic expansion in a turbine Process 4-1: constant-pressure heat rejection in a condenser Turbine Boiler Condenser Pump

Real Rankine Cycles Efficiency of Pump Efficiency of Turbine h 2’ = (h 2 – h 1 )/η p + h 1 h 4’ = h 3 – η p (h 3 – h 4 ) T S ’ 4’

Increase the Efficiency of a Rankine Cycle 1. Lowering the condenser pressure T S 2. Superheating the steam to a higher temperature 3. Increasing the boiler pressure

Ideal Reheat Rankine Cycles T S Turbine Boiler Condenser Pump Boiler Condenser Pump T S

Ideal Reheat Rankine Cycles q in = (h 3 – h 2 ) + (h 5 – h 4 ) q out = h 6 – h 1 T S w t = (h 3 – h 4 ) + (h 5 – h 6 ) w p = h 2 – h 1 = v(p 2 – p 1 )