ENGR 2213 Thermodynamics

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

First Law of Thermodynamics Closed Systems E: total energy includes kinetic energy, potential energy and other forms of energy All other forms of energy are lumped together as the internal energy U. Internal energy U is an extensive property. Specific internal energy u = U/m is an intensive property

Energy Analysis for a Control Volume Conservation of Mass Total Mass Leaving CV Total Mass Entering CV Net Change in Mass within CV - = Steady State

Steady-Flow Process Conservation of mass Conservation of energy

Steady-Flow Process For single-stream steady-flow process Conservation of mass Conservation of energy

Uniform-Flow Process Conservation of Mass Conservation of Energy + (m2u2 – m1u1)CV

Second Law of Thermodynamics Kelvin-Planck Statement It is impossible for any device that operates on a cycle to receive heat from a single reservoir and produce an equivalent amount of work. No heat engine can have a thermal efficiency of 100% The impossibility of having 100% efficiency heat engine is not due to friction or other dissipative effects.

Second Law of Thermodynamics Clausius Statement It is impossible to construct a device that operates on a cycle and produce no effect other than the transfer of heat from a low-temperature body to a high-temperature body. Equivalence of the two statements A violation of one statement leads to the violation of the other statement.

Second Law of Thermodynamics Carnot Principles • The efficiency of an irreversible heat engine is • always less than that of a reversible one • operating between the same two reservoirs. • The efficiencies of all reversible heat engines • operating between the same two reservoirs • are the same. A violation of either statement results in the Violation of the second law of thermodynamics.

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

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

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

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

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

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

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

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

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.

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

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

4 5 Boiler 3 6 P 2 Turbine FWH 5 2 T 7 Condenser P 1 4 1 6 3 2 1 7 S Ideal Regenerative Rankine Cycles Open Feedwater Heater

T 3 4 4 Boiler Turbine y 7 1-y 5 3 5 • 6 2 y 1-y Condenser 1 8 6 2 FWH 8 1 P 7 S Trap Ideal Regenerative Rankine Cycles Closed Feedwater Heater

Otto Cycles Nikolaus A. Otto (1876) – four-stroke engine Beau de Rochas (1862)

Diesel Cycles Rudolph Diesel (1890)

Brayton Cycles

ENGR 2213 Thermodynamics