Physics 262/266 GMUiitGeorge Mason n versity Prof. Paul So Chapter 19: The 1 st Law of Thermodynamics ? Heat, Work, and Paths in Thermodynamic Processes ? Internal Energy and the 1 st Law of Thermodynamics ? Types of Thermodynamic Processes ? More on Heat Capacities ? Adiabatic Processes Thermodynamic Systems ll i f bj? A Thermodynamic System: Any co ect on o o ects (considered as one ?system?) that may have potential to exchange energy with its surrounding.ggy ? System States & Thermodynamic Processes: ?State of a thermodynamic system is P characterized by a set of marcoscopic variables (P, V, T, n ) and, it can be visualized as a point * in the PV diagram. state 1 ?A thermodynamic system changes from one state (1) to another state (2) through a thermod namic process idi tdb th state 2 y process indica e y the blue curve/path in the PV diagram. V Thermodynamic Systems ? Notes: ? Thermodynamic states can only be specified if the system is in thermal equilibrium! (Every subparts of the system equilibrium (Every subparts of the should have the same values of P,T,V,n, etc.) ? A path for a thermodynamic process can only be represented in the PV diagram if the process is reversible (quasi-static). ? A quasi static process can be thought of as a sufficiently - sufficiently slow (still fast in macroscopic time) process such that the system is approximately near equilibrium at each step. Reversible vs. Non-Reversible Processes Reversible (Quasi-static) Non-Reversible (Non-Quasi-static) same initial & final states state 1 P Small changes in forcing the piston can NO small changes can stop the gas in filling state 1 P state 2 V increase/decrease the volume reversibly . pg the container after the partition is broken. state 2 V Energy Transfer in a Thermodynamic gy System Heat (Q): A thermodynamic system can absorb or release heat during a thermodynamic process. Work (W): Work is either done on or done by a system during a thermodynamic gy process. Note: Play attention to the Play attention to the sign conventions for Q and W! Work Done by a Gas The system (the gas) exerts a force (F = pA) on its surrounding (the piston) through a distance dx . The infinitesimal work done by the system dW is given by: dW = Fdx= PA d x = PdV F dx dx P dV Work Done by a Gas Ffiih ihl fV V hlkdiiFor a fin te c ange n t e vo ume rom 1 to 2 , the total wor one s g ven by integrating the differential: 2 V WpdV? ? 1 V Work Done by a Gas ( i d )Case 1: isochoric processes V s constant, dV=0 0W ? Case 2: isobaric processes (P is constant) 21 ()WPVV? ? Case 3: isothermal processes (T is constant) Example 19.1 2 1 V V WPdV? ? Starting with Using the Ideal Gas law: PV=nRT Work Done by a Isothermal Process We have, 2 1 V V nRT WdV V ? ? T is constant and we can pull it out of the integral together with the other two constants nR (fixed amount of gas), 2 1 2 1 ln V V VdV WnRT nRT VV ?? ?? ?? ?? ? For T constant, we also have 21 11 2 2 12 VP PV PV or VP ? ? ?? So, we can also write, 1 2 ln P WnRT P ? ?? ?? Work Done is Path Dependent Work done by a gas is different depending on path taken even though the starting and ending states are the same for all these processes. Heat Absorbed/Release is also Path bso so Dependent Process 1 (isothermal expansion) Process 2 (free expansion) Starting and ending states are the same for both processes! Internal Energy (U) Internal Energy (U): the total amount of energy (KE + PE) intrinsic to the system associated with all its microscopic components when viewed in a reference frame at rest with the object. system The KE and PE associated with the bulk motion are NOT parts of the internal energy U of the v system. Internal Energy (example) li l il A bucket of water KEs: translationa :rotaional: vibrational: PEs: ithi l l bt l l @ rest on the table w n mo ecu es: between mo ecu es: molecular bonds dipole-dipole interactions Internal Energy for an Ideal Gas Recall in an Ideal Gas? We have explicitly calculated its Internal Energy U: ? 3 translational degrees of Nit l l translational degrees freedom only! ? N molecules ? hib˝kT No in ermo ecu ar forces each contributes 13 3 22 UNkT NkT ?? ?? ?? ?? (Ideal Gas monoatomic) The Internal Energy for an Ideal Gas U is a function of T ONLY! (Experimentally, this is also shown to be the case for most diluted gases!) The 1 st Law of Thermodynamics hhbhdkhhilWe have seen that ot heat an wor can c ange t e nterna energy of the system. In particular, Wk Heat W Work +Q - Piston pushing down on gas H tth t Wkdtht eat enters the sys em, U increases (?U > 0) Work done on the sys em, U increases (?U > 0) The 1 st Law of Thermodynamics Putting both of these mechanisms together, we can combine them into one mathematical statement for the change in U in any processes, UQW? ?? (1 st Law of Therm.) This is a generalization of the principle of conservation of energy to include energy transfer through heat as well as through mechanical means (work). IttPtf?U Although both Q and W are path/process dependent, ?U is id d fhU i tt ibl ditd d Importan roper y or indepen ent of path. s a state variable and it depen s on the initial and final states only. 1 st Law of Thermodynamics ?U can be positive, negative, and zero. Special Processes 1. Isolated Systems (no interactions with surrounding) Since Q = W = 0, 0U? ? U remains a constant in an isolated system. 2. Cyclic Processes (starting state = end state) Since U is a state variable, ?U = 0. P 0UQW? ??? 1 st Law gives, QW(ildb) V ? (= area encirc e y curve Administrator Microsoft PowerPoint - ch19_young_freedman.ppt [Compatibility Mode]
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