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Heat & The First Law of Thermodynamics
Chapter 17 Heat & The First Law of Thermodynamics
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Breaking of equilibrium changing of state
Thermal processes Breaking of equilibrium changing of state If the process is extremely slow, or quasi-statical system always at equilibrium state in the process Shown in PV diagram P V 2 1 Point: equilibrium state Curve: quasi-statical process 2
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Heat as energy transfer
Heat is not a fluid substance and not even a form of energy calorie: amount of heat to raise 1g water by 1℃ Joule’s theory & mechanical equivalent of heat Heat is energy that transferred from one body to another because of a difference in temperature
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The sum total of all the energy of all molecules
Internal energy The sum total of all the energy of all molecules —— thermal energy / internal energy Temperature, heat and internal energy Internal energy of monatomic (1-atom) ideal gases: n-atoms molecule, real gases, liquids & solids 4
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The first law of thermodynamics
The change in internal energy of a closed system, will be equal to the heat added to the system minus the work done by the system. This is the first law of thermodynamics where Q is the net heat added to the system and W is the net work done by the system U is a state variable, but Q and W are not 5
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Consider the gas in a cylinder with a piston
Calculating the work Consider the gas in a cylinder with a piston Work done by the gas to move the piston dx : dx . . . P S dV For a finite change in volume from VA to VB : B A P V 6
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Heat in process Example1: In process abc, 800J heat flow into the system, and 500J work done by system. In process cda, 300J work done to system, What’s the heat? Solution: First law P V a b c d ΔU is different! 7
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Isothermal process: ( constant T )
3 simple processes Isothermal process: ( constant T ) B A P V VA VB Isobaric process: ( constant P ) P V VA VB A B C Isochoric process: ( constant V ) 8
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Adiabatic process: ( Q = 0 )
No heat is allowed to flow into or out of system Well insulated or process happens too quickly Adiabatic curve is steeper than an isothermal curve B A P V isothermal C adiabatic Temperature decreases as well 9
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Solution: In process ab:
Cyclic process Example2: An monatomic (1-atom) gas system goes through processes ab, bc, ca. Determine Q, W and ΔU in each process. Solution: In process ab: c P (105Pa) 4 V ( l ) 2 o a b 1 3 10
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In process bc: In process ca: P (105Pa) c b a o Q, W and ΔU
4 V ( l ) 2 o a b 1 3 In process ca: Q, W and ΔU in process abca? 11
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Heat transfer in → temperature rises
Specific heat Heat transfer in → temperature rises c is called the specific heat of material For water at 15℃ and 1atm: one of the highest specific heats of all substance c as constant (P407, T17-1) except for gases 12
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c for gases depend on how the process goes on
Molar specific heat c for gases depend on how the process goes on Heat required to raise 1mol gas by 1℃ (conditions) Isochoric (constant V) CV: Isobaric (constant P) CP: For CV of monatomic (1-atom) ideal gas, W = 0 13
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What is CV of diatomic or triatomic gas?
Degrees of freedom What is CV of diatomic or triatomic gas? Degrees of freedom: number of independent ways molecules can possess energy. monatomic: i = 3 diatomic: i = 5 triatomic: i = 6 14
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Equipartition of energy
Principle of Equipartition of energy: Energy is shared equally among the active degrees of freedom, each degree of freedom of a molecule has on the average energy equal to kT/2. Average energy of a molecule: Internal energy: 15
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CV of diatomic gases by experiments:
Active DoF & CV CV of diatomic gases by experiments: Active degrees of freedom at different T Translational motion; Rotation; Vibration i = 3, 5, 6 for 1, 2, n-atoms Isochoric molar specific heat: 16
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Solution: (a) Active degrees of freedom: i = 5
Energy in gas system Example3: Determine the internal energy of (a) 2l O2 gas system at 1atm; (b) same system at same T but O2 is dissociated to 2O. Solution: (a) Active degrees of freedom: i = 5 (b) O2 dissociate to 2O: i = 3 17
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Isobaric molar specific heat CP
In an isobaric process (constant P): Isobaric molar specific heat: Adiabatic coefficient 18
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Equation for adiabatic curve?
Adiabatic equation B A P V isothermal C adiabatic Equation for adiabatic curve? Equation of quasi-static adiabatic process 19
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1) Isothermal / adiabatic C ?
Some questions P V 1) Isothermal / adiabatic C ? 2) Why 3) Monatomic / diatomic / triatomic gas 4) Process AC is adiabatic adiabatic B A P V C D then does heat flow in or out in process AB and AD? 20
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Isobaric & adiabatic Example4: N2 system compresses isobarically in process AB, and then expands adiabatically to C. (a) Q in process AB; (b) PC ; (c) W in process BC. Solution: (a) (b) P V C A B 3V isothermal ? (c) 21
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Solution: No heat flows in or out → Q = 0
Free expansion Example5: 2 well-insulated container. A is filled with gas and B is empty. Open the valve, there is an adiabatic free expansion. What is the final P, T ? Solution: No heat flows in or out → Q = 0 No work is done → W = 0 U doesn’t change in free expansion! PA , TA , V V Not quasi-static, no PV diagram 22
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*Heat transfer Conduction: Convection: Radiation: 23
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