CHAPTER 3 The First Law of Thermodynamics: Closed Systems
Closed system Energy can cross the boundary of a closed system in two forms: Heat and work FIGURE 3-1 Specifying the directions of heat and work. 3-1
Heat Energy transfer by virtue of temperature difference. If there is no heat transfer during a process, then the process is called adiabatic. 3-
30 kj heat Q=30 kj M= kg Δt=5 s Q =6 kw q=15 kj/kg Heat transfer per unit mass Heat transfer rate (kj/kg) (kj/s or kw) Sign Convention for Heat Heat in Q=+5 kj (+) ve if to the system (-)ve if from the system Q= - 5kJ Heat out 3-3
System boundary A spring is doing work on the surroundings Work An energy interaction which is not caused by a temperature difference between a system and its surroundings.(a rising piston, a rotating shaft,etc.) (kj/kg) W=5kJ The work done per unit time is called power and denoted (kj/s or kw) Sign Convention of Work W=-5kJ (+)ve if work done by a system (-)ve if work done on a system 3-4
Moving boundary work (P dv work): The expansion and compression work in a piston-cylinder device. FIGURE 3- A gas does a differential amount of work dw b as it forces the piston to move by a differential amount ds. 3-5
FIGURE 3-3 The area under the process curve on a P-V diagram represents the boundary work. Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 3-6
FIGURE 3-4 The net work done during a cycle is the difference between the work done by the system and the work done on the system. Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 3-7
First Law of Thermodynamics or the Conservation of energy Principle: Net energy transfer to (or from) the system = As heat and work Net increase (or decrease) İn the total energy of the system Q W = ΔU 3-9
(Remember from chapter 1: ΔE = ΔU + ΔKE + ΔPE ) Q W = ΔU + ΔKE + ΔPE where ΔU = m( - ) ΔKE =1/ m( - ) ΔPE =mg( - ) (kj) Most closed systems encountered in practice are stationary i.e. ΔPE =0 ΔKE =0 Q W = ΔU 3-10
Example: System boundary Q W U 0 0 KE PE Wpw = 18.5kJ 5 kg of steam Wpiston ΔU = m(u - u1 ) W=Wpw +Wpiston Q -(Wpw +Wpiston)= m(u - u1 ) Q = 80 kj u 1 u 709.9 kj/kg 659.6 kj/kg (+80kJ) ( ( -18.5kJ)+ Wpiston=(5kg)(659.6-709.9)kJ/kg Wpiston =350kJ 3-1
Example: constant-pressure process, initially saturated water vapor. =? Q Wel = = -3.7 kj (-7.kJ)= 0.05 kg ( - 75.3 kj/kg) = 865.3 kj/kg =300 kpa = 865.3 =00ºC Table A-6 3-13 Note: for constant pressure case: Q W other = ΔH and W = W boundary + W other
Example: constant volume Superheated steam T 1 v Q 0 0 0 Q W U KE PE Q m( u ) u1 Note: for constant volume case: Q Wother U KE PE 3-14
Example: changing volume and pressure Evacuated system P 1 Q HO Partition V 0 0 0 Q W U KE PE Q m( u ) u1 note: u1 uf@tsat u = uf +xufg 3-15
Specific Heats The energy required to raise the temperature of a unit of a substance by one degree. Cv : specific heat at constant volume Cp : specific heat at constant pressure Helium gas: V=constant m=1kg ΔT=1ºC Cv=3.13 kj/kgºc P=const m=1kg ΔT=1ºC Cp=5. kj/kgºc () (1) Cp > Cv Because at constant pressure, the energy required for expansion work must also be supplied to system. 3.13kJ 5.kJ 3-16
First law for constant volume: First law for constant pressure: 3-17
Ideal Gases: Pv RT Joule demonstrated that for ideal gases u=u(t) Cv=Cv(T) h u Pv Pv RT h u RT Since R is constant and u=u(t) h=h(t) Cp=Cp(T) and 3-18
Three ways of calculating u and h h h h 1 from tables h h 1 c c p p, avg ( T ) T dt Similarly: 3-19
differentiate dt c p dt =c v dt+rdt On a molar basis Specific heat ratio 3-0
3-1 Solids and Liquids: Can be approximated as incompressible: Again, specific heats depend on temperature only. The change in internal energy between states 1 and : c c c v p ) ( ) ( 1 1 1 T T c u dt T c u u u avg
Example: insulated Q-W=ΔU or ΔU=0 m 50kg 80 o C Water 5ºC U U 0 mc( T T ) mc( T T ) m water iron 1 V v 5 C U iron water 0.5m 3 0.001m 3 1 water 0 500kg kg 0.5 Specific heats are determined from table A-3. 50 kg(0.45 kj kg ) T C o 80 o C 500kg(4.18 kj kg o )( T C 5 o C) 0 T 5.6 o C 3-