First Law of Thermodynamics

Transcription

1 First Law of Thermodynamics During an interaction between a system and its surroundings, the amount of energy gained by the system must be exactly equal to the amount of energy lost by the surroundings. Energy can cross the boundary of a closed system in two distinct forms: heat and work. Spring 003 ECE309: Chapter 3 Heat Transfer Heat is a form of energy that is transferred between a system and its surroundings by virtue of a temperature difference. A process during which there is no heat transfer is called an adiabatic process. An adiabatic process should not be confused with an isothermal process. Spring 003 ECE309: Chapter 3

2 Heat: Units & Direction Heat has energy units, kj (or Btu). The amount of heat transferred during a process between two states is denoted by Q or just Q. Heat transfer per unit mass of a system is denoted q as: Q q = kj/kg m Heat is a directional quantity. Heat transfer to a system is positive, and heat transfer from a system is negative. Spring 003 ECE309: Chapter 3 3 Modes of Heat Transfer Heat can be transferred in three different ways: conduction, convection, and radiation. All modes of heat transfer require the existence of a temperature difference. All modes of heat transfer are from the high-temperature medium to a lower temperature one. Spring 003 ECE309: Chapter 3 4

3 Conduction Heat Transfer Fourier s Law: Q cond T = ka x Thermal Conductivity or Q cond = ka dt dx (W) Spring 003 ECE309: Chapter 3 5 Convection Heat Transfer Convection is the mode of energy transfer between a solid surface and the adjacent liquid or gas which is in motion. It involves the combined effects of conduction and fluid motion. The faster the fluid motion, the greater the convection heat transfer. Spring 003 ECE309: Chapter 3 6 3

4 Forced vs.natural Convection Convection is called forced convection if the fluid is forced to flow by external means such as a fan, or a pump, Convection is called free or natural convection if the fluid motion is caused by buoyancy forces that are induced by density differences. QD conv = ha T ( s T f ) Spring 003 ECE309: Chapter 3 7 Heat Transfer Coefficient, h QC conv = ha T ( s T f ) h is a function of surface geometry, the nature of fluid motion, the properties of the fluid, and the bulk fluid velocity. Typical values of h, in W/(m.K): -5 free convection of gases, free convection of liquids, 5-50 forced convection of gases, 50-0,000 forced convection of liquids, ,000 convection in boiling and condensation processes. Spring 003 ECE309: Chapter 3 8 4

5 Radiation Heat Transfer Radiation is the energy emitted by matter in the form of electromagnetic waves (or photons) as a result of the changes in the electronic configurations of the atoms or molecules. Stefan-Boltzmann Law: Q = σ AT 4 emit, max s Q rad = ε σ A( T 4 s T 4 surr ) σ = 5.67 X 0-8 W/(m.K 4 ) 0 ε Temperatures are absolute! Spring 003 ECE309: Chapter 3 9 Example Given: A =.9 m h = 6 W/m.C Calculate total rate of heat transfer. Spring 003 ECE309: Chapter 3 0 5

6 Work Work is an energy interaction which is not caused by a temperature difference. Work is associated with a force acting through a distance (rising piston, rotating shaft, electric wire crossing the system boundaries). Work done by a system is positive, and work done on a system is negative. Spring 003 ECE309: Chapter 3 Similarities Both heat and work are boundary phenomena. Systems possess energy, but not heat or work. That is, heat and work are transfer phenomena. Both are associated with a process, not a state. Both are path functions. dv = V V = V δw = W NOT W Spring 003 ECE309: Chapter 3 6

7 Examples Q = 0 Q = 0 Q > 0 U = 0 W < 0 W = 0 Spring 003 ECE309: Chapter 3 3 Electrical Work In an electric field, electrons in a wire move under the effect of electromotive forces, doing work. W e = V N (kj) WC e = V I (kw) W e W e = V I dt = V I t (KJ) (KJ) Spring 003 ECE309: Chapter 3 4 7

8 Example Discuss the heat and work interactions for system A, B, and the combined system. Spring 003 ECE309: Chapter 3 5 Mechanical Work Work is force times displacement. W = Fds Requirements for a work interaction: () There must be a force acting on the boundary, and () The boundary must move. Spring 003 ECE309: Chapter 3 6 8

9 Moving Boundary Work It is associated with the expansion or compression of a gas in a pistoncylinder device, It is also called boundary work or PdV work, Moving boundary work is the primary form of work involved in automobile engines. Spring 003 ECE309: Chapter 3 7 Boundary Work (Quasi-Equilibrium Process) δw b = F ds = P Ads = P dv W b = PdV area = A = da = P dv Spring 003 ECE309: Chapter 3 8 9

10 Boundary Work (Quasi-Equilibrium Process) The boundary work done during a process depends on the path followed as well as the end states. The net work done during a cycle is the difference between the work done by the system and the work done on the system. Spring 003 ECE309: Chapter 3 9 Example Determine the work done during this process. Spring 003 ECE309: Chapter 3 0 0

11 Polytropic Process n+ n+ n V V P V P V Wb = P dv = CV dv = C = n + n W b mr ( T T ) =, n n Spring 003 ECE309: Chapter 3 Spring Work δ W spring = F dx (kj) For linear elastic springs: F = k x s (kn) k s = Spring constant (kn/m) W spring = k ( x x s ) Spring 003 ECE309: Chapter 3

12 Example Determine: (a) Final pressure inside the cylinder, (b) Total work done by the gas, and (c) Fraction of this work done against the spring to compress it. Spring 003 ECE309: Chapter 3 3 First Law of Thermodynamics Q = E Q = Qnet = E W e = E W PW = E Q = E when W = 0 W = E when Q = 0 Spring 003 ECE309: Chapter 3 4

13 First Law of Thermodynamics Net energy transfer to (or from) Net increase (or decrease) in the = the system as heat and work total energy of the system Q W = E (kj) Where: Q = Q in Qout W = W out Win E = E E Spring 003 ECE309: Chapter 3 5 First Law of Thermodynamics E = U + KE + PE Q W = U + KE + PE U = m( u ) u KE = / m( v v ) Where{ PE = mg( z ) z For Stationary Systems: Q W = U Spring 003 ECE309: Chapter 3 6 3

14 Other Forms of the First Law Per unit mass: In rate form: q w = e Q W = de dt (kj/kg) (kw) For cyclic processes: Q W =0 (kj) Spring 003 ECE309: Chapter 3 7 Specific Heats Specific heat is defined as the energy required to raise the temperature of a unit mass of a substance by one degree. Specific heat depends on how the process is executed. Specific heat at constant pressure C P is always greater than specific heat at constant volume C v. Spring 003 ECE309: Chapter 3 8 4

15 Specific Heats For a stationary closed system undergoing a constant-volume process: δ q δ wother = du C v dt = du C v = u T v C p = h T p Note that C v and C p are thermodynamic properties. They are both state functions. Spring 003 ECE309: Chapter 3 9 U, h, and C for Ideal Gases Joule s Experiment: P υ = h = u + RT u = u(t ) h = h(t ) Pυ h = u + RT du = Cv ( T ) dt dh = C p ( T ) dt u = u h = h u = C ( T dt v ) h = C p T ) ( dt Spring 003 ECE309: Chapter

16 Specific Heats of Ideal Gases Specific heats of gases with complex molecules are higher and increase with temperature. Variation of specific heats with temperature may be approximated as linear over small temperature intervals. Ideal-gas specific heats of monatomic gases remain constant over the entire temperature range. Spring 003 ECE309: Chapter 3 3 Specific Heats of Ideal Gases h = u + RT dh = du + R dt Cp = Cv + R (kj/kg.k) On a molar basis: C = C + R p v u (kj/kmol.k) Specific Heat Ratio: C k = C p v k =.667 Monatomic Gases (Ar) { k =.4 Diatomic Gases (Air) Spring 003 ECE309: Chapter 3 3 6

17 Example Determine the final temperature of the nitrogen. Spring 003 ECE309: Chapter 3 33 Example Determine: (a) Final temperature, (b) Work done by the air, (c) Total heat added. 350 kpa pressure is required to move the piston. Spring 003 ECE309: Chapter

18 u, h, and C of Solids and Liquids Solids and liquids are essentially incompressible. Cp = Cv = C (Solids& Liquids) du = C dt = C( T ) dt v h h = ( u u) + v( P P ) u = u u = C( T ) dt h = u + υ P The term (ν P) is often small compared with the first term ( u) and can be neglected without significant loss in accuracy. Spring 003 ECE309: Chapter 3 35 Example Determine the temperature when thermal equilibrium is reached. Spring 003 ECE309: Chapter