ENGR 2213 Thermodynamics

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

2. surroundings system 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

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

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

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

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

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

8. Isentropic Processes of Ideal Gases 1. Constant Specific Heats (a) R = cp – cv k = cp/cv R/cv = k – 1

9. Isentropic Processes of Ideal Gases 1. Constant Specific Heats (b) R = cp – cv k = cp/cv R/cp = (k – 1)/k

10. Isentropic Processes of Ideal Gases 1. Constant Specific Heats p1V1k = p2V2k Polytropic Processes pVn = constant n = 0 constant pressure isobaric processes n = 1 constant temperature isothermal processes n = k constant entropy isentropic processes n = ±∞ constant volume isometric processes

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

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

13. 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.

14. 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.

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

16. 3 T 2 Boiler 3 2 Pump Turbine 1 4 S 1 4 Condenser Ideal Rankine Cycles 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

17. T 3 2’ 2 1 4 4’ S Real Rankine Cycles Efficiency of Pump h2’ = (h2 – h1)/ηp + h1 Efficiency of Turbine h4’ = h3 – ηp(h3 – h4)

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

19. T 3 2 1 4 S 2 3 T 5 2 Boiler 3 Boiler 3 4 Pump 4 2 Pump Turbine 1 5 1 6 6 Condenser 1 4 S Condenser Ideal Reheat Rankine Cycles

20. 3 T 5 4 2 1 6 S Ideal Reheat Rankine Cycles wp = h2 – h1 = v(p2 – p1) qin = (h3 – h2) + (h5 – h4) wt = (h3 – h4) + (h5 – h6) qout = h6 – h1