Thermodynamics: An Engineering Approach 9th Edition Yunus A. Cengel, Michael A. Boles, Mehmet Kanoglu McGraw-Hill Education, 2019 Chapter 4 ENERGY ANALYSIS OF CLOSED SYSTEMS

Copyright McGraw-Hill Education. Permission required for reproduction or display. Objectives Examine the moving boundary work or P dV work commonly encountered in reciprocating devices such as automotive engines and compressors. Identify the first law of thermodynamics as simply a statement of the

conservation of energy principle for closed (fixed mass) systems. Develop the general energy balance applied to closed systems. Define the specific heat at constant volume and the specific heat at constant pressure.

Relate the specific heats to the calculation of the changes in internal energy and enthalpy of ideal gases. Describe incompressible substances and determine the changes in their internal energy and enthalpy. Solve energy balance problems for closed (fixed mass) systems that involve heat and work interactions for general pure substances, ideal gases, and incompressible substances.

2 MOVING BOUNDARY WORK Moving boundary work (P dV work): The expansion and compression work in a piston-cylinder device. Quasi-equilibrium process: A process during which the system remains nearly in equilibrium at all times. Wb is positive for expansion

Wb is negative for compression FIGURE 41 The work associated with a moving boundary is called boundary work. FIGURE 42 A gas does a differential amount of work WWb as it forces the piston to move by a differential amount ds. 3 FIGURE 43

The area under the process curve on a P-V diagram represents the boundary work. FIGURE 44 The boundary work done during a process depends on the path followed as well as the end states. The area under the process curve on a P-V diagram is equal, in magnitude, to the work done during a quasi-equilibrium expansion or 4

compression process of a closed system. Generalized boundary work relation Pi is the pressure at the inner face of the piston. FIGURE 45 The net work done during a cycle is the difference between the work done by the system and the work done on the system.

In a car engine, the boundary work done by the expanding hot gases is used to overcome friction between the piston and the cylinder, to push atmospheric air out of the way, and to rotate the crankshaft. 5 Boundary Work for a Constant-Pressure Process FIGURE 47

Schematic and P-v diagram for Example 42. 6 Boundary Work for a Constant-Volume Process FIGURE 46 Schematic and P-V diagram for Example 41. 7

Boundary Work for an Isothermal Compression Process FIGURE 48 Schematic and P-V diagram for Example 43. 8 Boundary Work for a Polytropic Process For ideal gas FIGURE 49

Schematic and P-V diagram for a polytropic process. 9 Expansion of a Gas against a Spring FIGURE 410 Schematic and P-V diagram for Example 44. 10 ENERGY BALANCE FOR CLOSED SYSTEMS Energy balance for any system

undergoing any process Energy balance in the rate form The total quantities are related to the quantities per unit time Energy balance per unit mass basis Energy balance in differential form Energy balance for a cycle 11

FIGURE 411 For a cycle E = 0, thus Q = W. 12 Energy balance when sign convention is used: - heat input and work output are positive - heat output and work input are negative FIGURE 412 Various forms of the first-law relation for closed systems. The first law cannot be proven mathematically, but no process in nature is known

to have violated the first law, and this should be taken as sufficient proof. 13 Energy balance for a constantpressure expansion or compression process General analysis for a closed system undergoing a quasi-equilibrium constant-pressure process. Q is to the system and W is from the system. For a constant-pressure expansion or compression process:

U Wb H 14 An example of constant-pressure process FIGURE 413 Schematic and P-v diagram for Example 45. 15 FIGURE 414

For a closed system undergoing a quasi-equilibrium, P = constant process, U + Wb = H. Note that this relation is NOT valid for closed systems processes during which pressure DOES NOT remain constant. FIGURE 416 Expansion against a vacuum involves no work and thus no energy transfer. 16

Unrestrained Expansion of Water FIGURE 415 Schematic and P-v diagram for Example 46. 17 SPECIFIC HEATS Specific heat at constant volume, cv: The energy required to raise the temperature of the unit mass of a substance by one degree as the volume is maintained constant.

Specific heat at constant pressure, cp: The energy required to raise the temperature of the unit mass of a substance by one degree as the pressure is maintained constant. FIGURE 417 It takes different amounts of energy to raise the temperature of different substances by the same amount. FIGURE 418 Specific heat is the energy required to raise the temperature of a unit mass of a substance by one degree in

18 a specified way. FIGURE 419 Constant-volume and constant-pressure specific heats cv and cp (values given are for helium gas). 19 Consider a fixed mass in a stationary closed system undergoing a constantvolume process

Consider a constant-pressure expansion or compression process The equations are valid for any substance undergoing any process. cv is related to the changes in internal energy and cp to the changes in enthalpy. FIGURE 420 Formal definitions of cv and cp. 20

True or False: cp is always greater than cv FIGURE 421 The specific heat of a substance changes with temperature. cv and cp are properties. The specific heats of a substance depend on the state. The energy required to raise the temperature of a substance by one degree is different at different temperatures and pressures. A common unit for specific heats is kJ/kgC or kJ/kgK. Are these units identical?

21 INTERNAL ENERGY, ENTHALPY, AND SPECIFIC HEATS OF IDEAL GASES Internal energy and enthalpy change of an ideal gas FIGURE 422 Schematic of the experimental apparatus used by Joule. Joule showed using this experimental

apparatus that u=u(T) 22 FIGURE 423 For ideal gases, u, h, cv, and cp vary with temperature only. 23 FIGURE 424 Ideal-gas constant-pressure specific heats for some gases (see Table A2c

for cp equations). 24 At low pressures, all real gases approach ideal-gas behavior, and therefore their specific heats depend on temperature only. The specific heats of real gases at low pressures are called idealgas specific heats, or zeropressure specific heats, and are often denoted cp0 and cv0. u and h data for a number of gases have been tabulated. These tables are obtained by

choosing an arbitrary reference point and performing the integrations by treating state 1 as the reference state. FIGURE 425 In the preparation of ideal-gas tables, 0 K is chosen as the reference temperature. 25 Internal energy and enthalpy change when specific heat

is taken constant at an average value FIGURE 426 For small temperature intervals, the specific heats may be assumed to vary linearly with temperature. FIGURE 427 The relation u = cv T is valid for any kind of process, constant-volume or not. 26 Three ways of calculating u and h

1. By using the tabulated u and h data. This is the easiest and most accurate way when tables are readily available. 2. By using the cv or cp relations (Table A-2c) as a function of temperature and performing the integrations. This is very inconvenient for hand calculations but quite desirable for computerized calculations. The results obtained are very accurate. 3. By using average specific heats. This is very simple and certainly very

convenient when property tables are not available. The results obtained are reasonably accurate if the temperature interval is not very large. FIGURE 428 Three ways of calculating u. 27 Specific Heat Relations of Ideal Gases The relationship between cp, cv and R

dh = cpdT and du = cvdT On a molar basis Specific heat ratio The specific ratio varies with temperature, but this variation is mild. For monatomic gases (helium, argon, etc.), its value is essentially constant at 1.667. Many diatomic gases, including air, have a specific heat ratio of about 1.4 at room temperature. 28

FIGURE 429 The cp of an ideal gas can be determined from a knowledge of cv and R. 29 Heating of a Gas in a Tank by Stirring FIGURE 430 Schematic and P-V diagram for Example 48. 30

Heating of a Gas by a Resistance Heater FIGURE 431 Schematic and P-V diagram for Example 49. 31 Heating of a Gas at Constant Pressure FIGURE 432 Schematic and P-V diagram for Example 410.

32 INTERNAL ENERGY, ENTHALPY, AND SPECIFIC HEATS OF SOLIDS AND LIQUIDS Incompressible substance: A substance whose specific volume (or density) is constant. Solids and liquids are incompressible substances. FIGURE 433 The specific volumes of incompressible substances remain constant during a process.

FIGURE 434 The cv and cp values of incompressible substances are identical and are denoted by c. 33 Internal Energy Changes 34 Enthalpy Changes The enthalpy of a compressed liquid

Usually amore accurate relation than 35 Cooling of an Iron Block by Water FIGURE 435 Schematic for Example 412. 36 Heating of Aluminum Rods in a Furnace

37 Summary Moving boundary work Energy balance for closed systems Specific heats Internal energy, enthalpy, and specific heats of ideal gases Internal energy, enthalpy, and specific heats of incompressible substances (solids and liquids) 38