1

Chapter 5 The First Law of Thermodynamics

Energy conservation law Need to consider conservation of matter in

advance5.1 The first law of thermodynamics for

a control mass undergoing a cycle

(system) Back to original state

2

The first law of thermodynamics states that during any cycle a system (control mass) undergoes, the cyclic integral of the heat is proportional to the cyclic integral of the work.

Cyclic integral

J the net work during the cycle

The net heat transfer during the cycle.Proportionality factor (depends on unit)

See Fig. 5.1 (P.97) Ex: Q: CalorieW: Joule

QWJ = 1 3

5.2 The First Law of Thermodynamics for a Change in State of a Control MassFig. 5.2

4

5

6

In thermodynamicsE = internal energy (U) + kinetic energy (KE)

+ potential energy (PE)E = U + KE + PE

7

dE = dU + d(KE) + d(PE)Q = dU + d(KE) + d(PE) + w

The first law of thermodynamics for a change of state (control mass)

The form of K.E. for a control massNo heat transfer Q = 0No change in internal energy dU = 0No change in potential energy dPE = 0

(elevation)8

W = - d(KE) = - F dxWork done on the system

F = ma = m = m = mv

d KE = F dx = mv dv = md = d(m )Control mass ()

KE =m

9

Q = 0 d(KE) = 0 (no kinetic energy)dU = 0W = -d(PE) = -F dzIf F = mg, then dz is the variation in elevationd(PE) = mg dz

= m Constant;independent of z

(PE)2 (PE)1 = mg(z2 z1)

10

dE = dU + mv dv + mg dzstate 1 state 2E2 E1 = U2 U1 +mv22/2 mv12/2 + mgz2

mgz1 = (U + mv2/ 2 + mgz)2- (U + mv2/ 2 + mgz)1

Q = dU + + d(mgz) +W

1Q2 = U2 U1 + m(v22-v12)/2 + mg(z2 z1) + 1W2

11

(1) 1Q2 - 1W2 = (U + mv2/ 2 + mgz)2 - (U + mv2/ 2 + mgz)1 = E2 E1

For control mass(2) Conservation of energy

Read the book (joint checking account shared by husband and wife); EpropertyQ and W must cross the boundary

transaction12

(3) The changes in internal energy, kinetic energy and potential energy.Not absolute values in U, KE and PE.If want to refer the absolute value in U, KE and PE reference state

13

5.3 Internal Energy (U) A Thermodynamic PropertyExtensive property (so does the KE and PE)u = U / m (specific internal energy)U: total internal energyu: internal energy per unit massU (u) Ex: Table B.1.1 (P.664) B.1.2 (P.668)

uf (internal energy of saturated liquid)ug (internal energy of saturated vapor)

14

U = Uliq + Uvapm u = mliq uf + mvap ugu = uf + x ufg where ufg = ug uf

Ex: 5.1 (P.102) ()Ex: 5.2 (P.102)In steam table, u = 0 for saturated liquid at

0.01. (designated)

15

16

5.4 Problem Analysis and Solution Technique

1. Control mass? Control volume?(fixed mass) (mass can cross the boundary)

2. Initial state properties3. Final state properties4. Process5. Draw a diagram in steps 2 to 46. What kind model can we use? Ideal gas equ. / Steam table

7. Analysis of the problem8. Solution techniqueHw 5.1 5.10 5.11Ex.5.3 (P.103)

17

18

5.5 Enthalpy (H) ------A Thermodynamic Property

For a control mass, KE = 0 and PE = 0 1Q2 = U2 U1+ 1W2

1W2 = If P = const. (P1 = P2 = P) (Fig.5.5;

P.106)

1W2 = P = P (V2 V1) = P2V2 P1V11Q2 = U2 U1+ P2V2 P1V1= (U2 + P2V2) - (U1 + P1V1)

19

1Q2 = H2 H1 (const. pressure process)

For saturated stateh = (1 x) hf + x hg

= hf + x hfg (hfg = hg - hf)

20

5.20 5.28 5.29

21

5.6 The Constant-Volume and Constant Pressure Specific Heats

no phase change (may be solid or liquid or gas) homogeneous phaseSpecific heat(C): the amount of heat required

per unit mass to raise the temperature by one degree.

d(KE) = 0d(PE) = 0Q = dU + W = dU + P dV

22

23

Q = dU + P dV= dU + d(PV) d(U + PV) = dH

Cv and Cp are thermodynamic properties(independent of processes) Fig. 5.7 (P.111)

Ex: 5.5 (P.111)For solid and liquid, v =const.(incompressible)

24

25

5.7 The Internal Energy, Enthalpy, and Specific Heat of Ideal Gases

Equation of state of ideal gasP v = R T (R = / M)

for an ideal gasu = f(T) internal energy is a function of

temperature only (pressure)

1843, Joule experiment (P.114)

26

Questions: (1) Is air an ideal gas?(2) Can it be really sure that no

change in temperature was found?

27

28

29

30

5.8 The First Law as A Rate Equation

31

5.9 Conservation of MassControl mass: fixed quantity of mass

Q: energy change (for a control mass)Whether the mass change?

32