Chapter 3 First Law of Thermodynamics and Energy Equation

Size: px

Start display at page:

Download "Chapter 3 First Law of Thermodynamics and Energy Equation"

Louise McLaughlin
5 years ago
Views:

1 Fundamentals of Thermodynamics Chapter 3 First Law of Thermodynamics and Energy Equation Prof. Siyoung Jeong Thermodynamics I MEE0-0 Spring 04

2 Thermal Engineering Lab. 3. The energy equation

3 Thermal Engineering Lab. 3

4 Thermal Engineering Lab. 4 E Internal Energy Kinetic Energy Potential Energy E U KE PE KE mv, PE mgz de du mvv d mgdz m( V V ) E E U U mg( z z) mv du d d mgz Q W m( V V ) U U mg z z Q W ( )

5 Thermal Engineering Lab. 5 Ex. 3. A tank containing a fluid is stirred by a paddle wheel. The work input to the paddle wheel is 5090 kj. The heat transfer from the tank is 500 kj. Consider the tank and the fluid inside a control surface and determine the change in internal energy of this control mass.

6 Thermal Engineering Lab The first law of thermodynamics For a control mass undergoing a cycle J Q W Q W

7 Thermal Engineering Lab. 7 For a change in state of a control mass Q W A B Q A Q B W A W B C B Q Q W W C B C B

8 Thermal Engineering Lab. 8 Q Q W W A C A C Q W Q W A A C C Q W depends only on the initial and final state not on the path. Q W de Q W E E

9 Thermal Engineering Lab The definition of work W F dx F d x W = +: done by a system 부호 W = - : done on a system J N m W W [ J / sec] [ W ] dt

10 Thermal Engineering Lab. 0

11 Thermal Engineering Lab. W F dx Frd Td W F dx Frd Td W dx d W F F V Fr T dt dt dt W w m

12 Thermal Engineering Lab. Ex. 3. A car of mass 00 kg drives with a velocity such that it has a kinetic energy of 400 kj (see Fig. 3.6). Find the velocity. If the car is raised with a crane, how high should it be lifted in the standard gravitational field to have a potential energy that equals the kinetic energy?

13 Thermal Engineering Lab. 3 Ex. 3.3 Consider a stone having a mass of 0 kg and a bucket containing 00 kg of liquid water. Initially the stone is 0. m above the water, and the stone and the water are at the same temperature, state. The stone then falls into the water. Determine ΔU, ΔKE, ΔPE, Q and W for the following changes of state, assuming standard gravitational acceleration of m/s. a. The stone is about to enter the water, state. b. The stone has just come to rest in the bucket, state 3. c. Heat has been transferred to the surroundings in such an amount that the stone and water are at the same temperature, T, state 4.

14 Thermal Engineering Lab Work done at the moving boundary of a simple compressible system F PA W F dx PAdx PdV dv : W dv : W : :

15 Thermal Engineering Lab. 5

Thermal Engineering Lab. 6 Ex. 3.4 Consider a slightly different piston/cylinder arrangement, as shown in Fig. 3.0.

16 Thermal Engineering Lab. 6 Ex. 3.4 Consider a slightly different piston/cylinder arrangement, as shown in Fig In this example, the piston is loaded with a mass m p, the outside atmosphere P 0, a linear spring, and a single point force F. The piston traps the gas inside with a pressure P.

17 Thermal Engineering Lab. 7 Ex. 3.5 Consider the system shown in Fig. 3., in which the piston of mass m p is initially held in place by a pin. The gas inside the cylinder is initially at pressure P and volume V. When the pin is released, the external force per unit area acting on the system (gas) boundary is comprised of two parts : P ext = F ext / A = P 0 + m p g / A Calculate the work done by the system when the piston has come to rest.

18 Thermal Engineering Lab. 8 Polytropic process work W W PdV C n dv V CV n V C n C V V n n dv n n n PV V n n V n n n PV ( V V ) n PV P n C n V Const. C PV PV n

19 Thermal Engineering Lab. 9 Chapter 3. First law of thermodynamics and energy equation n P P PV n P P PV n V V PV n n n n n n n n n P P V V P P P P V V PV PV

20 Thermal Engineering Lab. 0 PV const. PdV C lnv V C ln V PV PV C dv V PV V ln V P ln P PV

Thermal Engineering Lab. Ex. 3.6 Consider as a system the gas in the cylinder shown in Fig. 3.4; the cylinder is fitted with a piston on which a number of small weights are placed.

21 Thermal Engineering Lab. Ex. 3.6 Consider as a system the gas in the cylinder shown in Fig. 3.4; the cylinder is fitted with a piston on which a number of small weights are placed. The initial pressure is 00 kpa, and the initial volume of the gas is 0.04 m 3. a. Let the Bunsen burner be placed under the cylinder, and let the volume of the gas increase to 0. m 3 while the pressure remains constant. Calculate the work done by the system during this process. b. Consider the same system and initial conditions, but at the same time that the Bunsen burner is under the cylinder and the piston is rising. Remove weights from the piston at such a rate that, during the process, the temperature of the gas remains constant. Calculate the work.

22 Thermal Engineering Lab. Ex. 3.6 (cont d) c. Consider the same system, but during the heat transfer remove the weights at such a rate that the expression PV.3 = constant describes the relation between pressure and volume during the process. Again, the final volume is 0. m 3. Calculate the work. d. Consider the system and initial state given in the first three examples, but let the piston be held by a pin so that the volume remains constant. In addition, let heat be transferred from the system until the pressure drops to 00 kpa. Calculate the work.

23 Thermal Engineering Lab Definition of heat Heat : Temp. difference 에의해전달되는에너지 Sign +: to a system -: from a system

24 Thermal Engineering Lab Heat transfer modes Conduction Q ka dt dx Convection Q AhT Radiation Q AT s 4

25 Thermal Engineering Lab. 5 Ex. 3.7 Consider the constant transfer of energy from a warm room at 0 inside a house to the colder ambient temperature of -0 through a single-pane window, as shown in Fig The temperature variation with distance from the outside glass surface is shown by an outside convection heat transfer layer, but no such layer is inside the room (as a simplification). The glass pane has a thickness of 5 mm (0.005 m) with a conductivity of.4 W/m K and. The outside wind is blowing, so the convective heat transfer coefficient is 00 W/m K. With an outer glass surface temperature of., we would like to know the rate of heat transfer in the glass and the convective layer.

26 Thermal Engineering Lab Internal energy a thermodynamic property U : U m u : Intensive property U mu u U u liq m f f U u f xu vap ( x) u m f fg g u g xu g

27 Thermal Engineering Lab. 7 Ex. 3.8 Determine the missing property (P, T, or x) and v for water at each of the following states: a. T = 300, u = 780 kj/kg b. P = 000 kpa, u = 000 kj/kg

Thermal Engineering Lab. 8 3.8 Problem analysis and solution technique Ex. 3.9 A vessel having a volume of 5 m 3 contains 0.

28 Thermal Engineering Lab Problem analysis and solution technique Ex. 3.9 A vessel having a volume of 5 m 3 contains 0.05 m 3 of saturated liquid water and 4.95 m3 of saturated water vapor at 0. MPa. Heat is transferred until the vessel is filled with saturated vapor. Determine the heat transfer for this process.

29 Thermal Engineering Lab. 9 Ex. 3.0 The piston/cylinder setup of Example 3.4 contains 0.5 kg of ammonia at -0 with a quality of 5%. The ammonia is now heated to +0, at which state the volume is observed to be.4 times larger. Find the final pressure, the work the ammonia produced, and the heat transfer.

30 Thermal Engineering Lab. 30 Ex. 3. The piston/cylinder setup shown in Fig. 3.0 contains 0. kg of water at 000 kpa, 500. The water is now cooled with a constant force on the piston until it reaches half of the initial volume. After this, it cools to 5 while the piston is against the stops. Find the final water pressure and the work and heat transfer in the overall process, and show the process in a P-v diagram.

31 Thermal Engineering Lab The thermodynamic property enthalpy P const, PE KE 0인 경우 Q U U W W P( V V ) Q U U PV PV ( U PV ) ( U PV ) H h U PV u Pv h h ( x) h h f xh f fg xh g

32 Thermal Engineering Lab. 3 Ex. 3. A cylinder fitted with a piston has a volume of 0. m3 and contains 0.5 kg of steam at 0.4 MPa. Heat is transferred to the steam until the temperature is 300, while the pressure remains constant. Determine the heat transfer and the work for this process.

33 Thermal Engineering Lab The constant-volume and constant-pressure specific heats Chapter 3. First law of thermodynamics and energy equation VdP dh Q PdV du W du Q P P P P v v v v T h T H m T Q m C T u T U m T Q m C CdT du dh vdp du Pv d du dh ) ( Solid and Liquids

34 Thermal Engineering Lab. 34

35 Thermal Engineering Lab The internal energy, enthalpy, and specific heat of ideal gas Generally u du T v u dt u( T, v) u v T dv

36 Thermal Engineering Lab. 36 Experiment of Gay-Lussac Q U U W U U U ( T, V V ) U ( T ) g A B W 실험결과, U ( T, V ) U ( T ) 0 g A W U ( T, V V ) U ( T, V ) u v g A B g A T 0 T T du du u T mc dt v v0 dt C dt v

37 Thermal Engineering Lab. 37

38 Thermal Engineering Lab. 38

39 Thermal Engineering Lab. 39 Chapter 3. First law of thermodynamics and energy equation ) ( ) ( T f h RT T u Pv u h dt C dh T h C P P P 0 R C C R C C RdT dt C C RdT du dh RT u pv u h v P v P v P ) (

40 Thermal Engineering Lab. 40 Ex. 3.3 Calculate the change of enthalpy as kg of oxygen is heated from 300 to 500 K. Assume ideal gas behavior.

41 Thermal Engineering Lab. 4 Ex. 3.4 A cylinder fitted with a piston has an initial volume of 0. m3 and contains nitrogen at 50 kpa, 5. The piston is moved, compressing the nitrogen until the pressure is MPa. and the temperature is 50. During this compression process heat is transferred from the nitrogen, and the work done on the nitrogen is 0 kj. Determine the amount of this heat transfer.

42 Thermal Engineering Lab. 4 Ex. 3.5 A 5 kg cast-iron wood-burning stove, shown in Fig. 3.7, contains 5 kg of soft pine wood and kg of air. All the masses are at room temperature, 0, and pressure, 0 kpa. The wood now burns and heats all the mass uniformly, releasing 500 W. Neglect any air flow and changes in mass and heat losses. Find the rate of change of the temperature (dt/dt) and estimate the time it will take to reach a temperature of 75.

43 3. General system that involve work. Wire W dl T Ee A. Surface Tension W S da Thermal Engineering Lab. 43

44 Thermal Engineering Lab. 44 Ex. 3.6 During the charging of a storage battery, the current i is 0 A and the voltage ε is.8 V. The rate of heat transfer from the battery is 0 W. At what rate is the internal energy increasing?

45 Thermal Engineering Lab. 45

46 Thermal Engineering Lab Conservation of mass E mc ( c velocity of light, E energy )

47 Thermal Engineering Lab. 47 Ex. 3.7 Consider kg of water on a table at room conditions 0, 00 kpa. We want to examine the energy changes for each of three processes: accelerate it from rest to 0 m/s, raise it 0 m, and heat it 0.

48 Thermal Engineering Lab Engineering applications

49 Thermal Engineering Lab. 49

KNOWN: Data are provided for a closed system undergoing a process involving work, heat transfer, change in elevation, and change in velocity.

KNOWN: Data are provided for a closed system undergoing a process involving work, heat transfer, change in elevation, and change in velocity. Problem 44 A closed system of mass of 10 kg undergoes a process during which there is energy transfer by work from the system of 0147 kj per kg, an elevation decrease of 50 m, and an increase in velocity