1 Chapter 13 temperature, heat transfer, and first law of thermodynamics Thermodynamics study the thermal energy (often called the internal energy) of systems. The central concept of thermodynamics is temperature. Temperature is one of the seven SI base quantities. What is temperature? Sense of hot and cold is not always reliable. 2 § 13.1 Some important concepts 1. The simple thermodynamic system A thermodynamic system is defined as a collection of many particles such as atoms and/or molecules. A simple thermodynamic system is a system that is macroscopic, homogeneous, isotropic, uncharged, chemically inert, and experiences no change in its total mechanical energy. The system is sufficiently large that surface effects can be neglect. No electric or magnetic fields are present, and gravitational fields are irrelevant. 2. Thermal equilibrium Put two system in thermal contact, after long enough time, if their properties (for instance: the temperature) do not change, they are in thermal equilibrium. 3. The zeroth law of thermodynamics § 13.1 Some important concepts 3 If body A and B are each in thermal equilibrium with a third body T, then they are in thermal equilibrium with each other. Every body has a property called temperature. When two bodies are in thermal equilibrium, we say that they have same temperature. And vice versa. 4. Temperature There exists a scalar quantity called temperature, which is a property of all thermodynamics systems in equilibrium. Two systems are in thermal equilibrium if and only if their temperatures are equal. § 13.1 Some important concepts Measuring temperature: 1types of thermometer By using some physical properties of matter— thermometric property that change with temperature. Volume of mercury—common household and laboratory thermometers. Constant volume gas thermometer: as shown in Figure § 13.1 Some important concepts 4 Platinum resistance thermometers—electrical resistance as a thermometric property Thermocouple—different thermal properties of two kind of metal § 13.1 Some important concepts 2Calibrating thermometers CYtXtCYtXt YY YY Yt XX XX Xt oo 100)()(0)()( )(100 )( )(100 )( 10010000 0100 0 0100 0 ==== ? ? = ? ? = § 13.1 Some important concepts 5 3 Ideal gas temperature scale (Kelvin scale) How to avoid the dependence of the particular means or substance? The triple point of water: t=0.01oC, T=0K R. Boyle: ttancons=PV L. J. Gay-Lussac: )1( 0 tVV V α+= J. A. C. Charles: )1( 0 tPP P α+= When P 0 ?0 C15.273 /1 0 0 o = === T T PV ααα § 13.1 Some important concepts For all kind of gas, when m is decrease, P 0 ?0. C15.273 /1 0 0 o = === T T PV ααα )1( 0 tPP P α+= mP ∝ 0 The intercept of the line on the axis t is . P α/1 § 13.1 Some important concepts Experiments: 0 100 o C/t P 0 T? Gas 1 Gas 2 Gas 3 0 P 6 T=0K is called absolute zero. One Kelvin is defined to be 1/273.16 of the temperature of the triple point of water. Ideal gas temperature scale: )lim(K16.273 3 0gas P P T → = K)(15.273 celsius += tT § 13.1 Some important concepts § 13.2 Heat transfer, and calorimetry 1. Heat and heat transfer Heat is energy that flow between a system and its environment simply because of the difference of temperature between them. Characteristic: 1the process of heat transfer continues until the both systems reach to thermal equilibrium (have same temperature); 2heat transfer occurs from the hotter system to the cooler system; 3heat transfer is essentially a microscopic atom-to-atom transfer of energy, it is distinctly different from macroscopic wok. 7 Q < 0, heat transfer from a system; Q > 0, heat transfer to a system. 2. Temperature change and specific heat Experiment: m Q T d d ∝ TcmQ dd = T Q m c d d1 = --specific heat [J/kg·K] § 13.2 Heat transfer, and calorimetry TncTcmQ ddd molar == T Q n c d d1 molar = --molar specific heat[J/mol·K] Molar specific heat is the heat transfer to one mole of the material needed to raise it temperature by one Kelvin. VV T Q m c ) d d ( 1 =For gases: PP T Q m c ) d d ( 1 = V T Q n c ) d d ( 1 Vmolar = P T Q n c ) d d ( 1 Pmolar = § 13.2 Heat transfer, and calorimetry 8 Notice: 1the specific heat of a substance usually varies with the temperature; 2in this text , we consider the specific heat to be independent of temperature. 3. Changes of phase and latent heat 1first-order phase transitions The phase transitions involved latent heats are called first-order phase transitions. For instance: converting water at 100oC to steam at 100oC. § 13.2 Heat transfer, and calorimetry Latent heat—the heat transfer needed to change the phase of a substance. 2second-order phase transitions The phase transitions that have zero latent heats are called second-order phase transitions. 3latent heat (heat of fusion and heat of vaporization) molar or nLQmLQ == Example: P605 13.12 § 13.2 Heat transfer, and calorimetry 9 § 13.3 mechanisms of heat transfer 1. reservoirs Reservoir is a special thermodynamics system. When a system in thermal contact with a reservoir experiences heat transfer to or from the system until it has the same temperature as the reservoir. The temperature of the reservoir does not change. 0thenif →?>> =?∴?= TQcm cm Q TTcmQQ 2. Mechanisms of heat transfer 1conduction Heat transfer by conduction depends on critically on the material bridging or connecting the warmer and cooler regions. Heat flow: x T kA t Q d d d d ?= k—thermal conductivity x T d d --Temperature gradient A—the the area of thermal contact § 13.3 mechanisms of heat transfer 10 For a steady state: =?= s x T d d constant d ∫∫ ?= xT T xsT H 0 dd d TT x TT s CHH ? = ? = R TT A d TT kA t Q CHCH ? = ? = d d k d R = --thermal resistance § 13.3 mechanisms of heat transfer For material in series: total21 d d R TT A RR TT A t Q CHCH ? = + ? = N RRRR +++= L 21total 1 d 2 d § 13.3 mechanisms of heat transfer 11 For material in parallel: ))(( ) d d () d d () d d ( 2 2 1 1 2 2 1 1 21total R A R A TT R TT A R TT A t Q t Q t Q CH CHCH +?= ? + ? = += 2convection(omit) 4 4 d d d d TaA t Q TeA t Q σ σ = ?= 3radiation --Radiation ---absorb § 13.3 mechanisms of heat transfer § 13.4 energy conservation: the first law of thermodynamics and the CWE theorem 1. Thermodynamics process A thermodynamics process is any way that a system changes from one state of thermal equilibrium to another such state. 2. Quasi-static(reversible) processes If a thermodynamics system undergoes a change from one state of thermal equilibrium to another slowly enough so at any instant the entire system essentially is in thermal equilibrium, then we say the process is quasi-static process. 12 3. Irreversible processes Any process that is not quasi-static process and reversible is called irreversible. In nature, all thermodynamic processes really are irreversible. 4. Energy 1macroscopic energy PEKEE += 2microscopic energy—internal energy U E—ordered energy U—disordered energy ?E and ?U is significant. § 13.4 energy conservation: the first law of thermodynamics and the CWE theorem 3The mechanisms of energy transfer Heat transfer to a system (conduction, convection, radiation), instigated by temperature differences: Microscopic mechanism Work done on the system, instigated by macroscopic forces: Macroscopic mechanism Notice: Q is not a state variable, the internal energy U is a state variable. § 13.4 energy conservation: the first law of thermodynamics and the CWE theorem 13 5. Fundamental energy conservation law EUWQ ?+?= ′ + Q—heat transfer W ′--work done on the system by external macroscopic, nonconservative forces ?E= ? KE+?PE—change in mechanical energy of the system ?U—change in the internal energy Pure classical mechanics: EPEKEW UQ ?=?+?= ′ =?= 00 § 13.4 energy conservation: the first law of thermodynamics and the CWE theorem Pure thermodynamics (simple system): WW UWQE ?= ′ ?= ′ +=? 0 WUQ +?= First law of thermodynamics: W—work done by the system on the surroundings Notice: 1It is a statement of conservation of energy for pure thermodynamic system; § 13.4 energy conservation: the first law of thermodynamics and the CWE theorem 14 2?E=0, there is no changes in sum of the macroscopic kinetic and potential energy of the system; 3Q>0, heat transfer to the system, W>0, the work done by the system on its surrounding environment; 4both the heat transfer to the system and the work done by the system depend on the particular way the system interacts with its environment. Notice: § 13.4 energy conservation: the first law of thermodynamics and the CWE theorem 6. The connection between the CWE theorem and the general statement of energy conservation For an inelastic collision of two particles: 2 22 )( 2 1 2 1 )( 2 1 ? )( ? mv mM M mvvmME iv mM m v vmMimv + ?= ? ′ +=? + = ′ ′ += r r CWE theorem: EW ?= ′ § 13.4 energy conservation: the first law of thermodynamics and the CWE theorem m M v r 15 but 00 ≠?=′+′=′ EWWW NG Use the general statement of energy conservation EUWQ ?+?= ′ + KEEU WQ ??=??=? = ′ = 00 2 )( 2 1 mv mM M U + =? Conclusion: the missing kinetic energy appears as an increase in the internal energy of the system. § 13.4 energy conservation: the first law of thermodynamics and the CWE theorem § 13.5 work done by ideal gases in some special processes 1. Ideal gas Experiments show that: at low enough density, all gases tend to obey the relation NkTnRTPV == KJ/mol32.8 ?=R Gas constant J/K1038.1 23? ×== A N R kBoltzmann constant 2. Wok done by a system rFW r r dd ?= 16 ∫ = =?= f i V V VPW VPidxiPAW d d ?? d xd F r x W>0 i V f V Work done by the system § 13.5 work done by ideal gases in some special processes W<0 i V f V net W Work done on the system Work done by the system in a cycle process § 13.5 work done by ideal gases in some special processes 17 Work is not state variable § 13.5 work done by ideal gases in some special processes 3. Work done by ideal gas at special processes 1at constant volume (isochoric process) 0dd f i V V === ∫∫ VPWW i V P V 2at constant pressure (isobaric process) )( dd if V V VVP VPWW f i ?= == ∫∫ i V P V f V § 13.5 work done by ideal gases in some special processes 18 3at constant temperature (isothermal process) 4in thermal isolation (adiabatic process) i f V V V V V V nRT V V nRT VPWW f i f i ln d dd = = == ∫ ∫∫ i V P V f V γ γ γ γ V VP PPVVP ii ii == )( 1 dd 11 γγ γ γ γ γ ?? ? ? === ∫∫ fi ii V V ii V V VV VP V V VP VPW f i f i § 13.5 work done by ideal gases in some special processes i V P V f V )( 1 1 ]1)[( 1 1 ffii f iii VPVP V VVP W ? ? = ? ? = ? γ γ γ § 13.5 work done by ideal gases in some special processes