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Chapter 19 The First Law of Thermodynamics Lecture by Dr. Hebin Li Assignment Due at 11:59pm on Sunday, December 7 HW set on Masteringphysics.com Final exam: Time: 2:15pm~4:15pm, Monday, December 8. Location: Green Library 100 On all chapters PHY 2048, Dr. Hebin Li Physics II (spring 2015) Physics with calculus II in spring 2015. PHY 2049-(U02 ~ U07) Lecture: Mondays 8:00 am ~ 9:40 am, AHC3-110 Recitation: Wednesdays 2:00 pm ~ 3:50 pm, locations vary Textbook: University Physics (13th edition) by Sears & Zemansky, Volume II (Chapter 21 ~ 36) Masteringphysics will be needed for HW. PHY 2048, Dr. Hebin Li Goals for Chapter 19 To represent heat transfer and work done in a thermodynamic process and to calculate work To relate heat transfer, work done, and internal energy change using the first law of thermodynamics To distinguish between adiabatic, isochoric, isobaric, and isothermal processes To understand and use the molar heat capacities at constant volume and constant pressure To analyze adiabatic processes PHY 2048, Dr. Hebin Li Thermodynamics systems A thermodynamic system is any collection of objects that may exchange energy with its surroundings. In a thermodynamic process, changes occur in the state of the system. Careful of signs! Q is positive when heat flows into a system. W is the work done by the system, so it is positive for expansion. PHY 2048, Dr. Hebin Li Work done during volume changes Macroscopic picture: Microscopic picture: The work done by the gas as the piston moves 𝑑𝑥 Since Then 𝑑𝑊 = 𝐹𝑑𝑥 = 𝑝𝐴𝑑𝑥 𝑑𝑉 = 𝐴𝑑𝑥 𝑑𝑊 = 𝑝𝑑𝑉 𝑊= 𝑉2 𝑝𝑑𝑉 𝑉1 If the pressure is constant 𝑊 = 𝑝(𝑉2 − 𝑉1 ) PHY 2048, Dr. Hebin Li Work on a pV diagram The work done equals the area under the curve on a pVdiagram. Work is positive for expansion and negative for compression. PHY 2048, Dr. Hebin Li Work depends on the path chosen When a thermodynamic system changes from an initial state to a final state, it passes through a series of intermediate states. This series of states is the path of the process. The work done by the system depends not only on the initial and final states, but also on the intermediate states, i.e. the path. PHY 2048, Dr. Hebin Li Internal Energy The internal energy of a system is the sum of the kinetic energies of all particles in the system, plus the sum of all the potential energies of interaction among these particles. It is not practical to calculate or measure the absolute internal energy. The change in internal energy depends on the heat transfer and work done 𝑈2 − 𝑈1 = ∆𝑈 = 𝑄 − 𝑊 (First law of thermodynamics) PHY 2048, Dr. Hebin Li First Law of Thermodynamics First law of thermodynamics: The change in the internal energy U of a system is equal to the heat added minus the work done by the system: U = Q – W. The first law of thermodynamics is just a generalization of the conservation of energy. Both Q and W depend on the path chosen between states, but U is independent of the path. If the changes are infinitesimal, we write the first law as dU = dQ – dW. PHY 2048, Dr. Hebin Li Cyclic processes and isolated systems • In a cyclic process, the system returns to its initial state. The internal energy change is zero. Then 𝑈2 = 𝑈1 and 𝑄 = 𝑊. • A isolated system does no work and has no heat flow in or out. That is 𝑊 = 𝑄 = 0 and ∆𝑈 = 0 Heat transfer and work in the process aba. PHY 2048, Dr. Hebin Li Four kinds of thermodynamics processes Adiabatic: No heat is transferred into or out of the system, so Q = 0. Isochoric: The volume remains constant, so W = 0. Isobaric: The pressure remains constant, so W = p(V2 – V1). Isothermal: The temperature remains constant. PHY 2048, Dr. Hebin Li Internal energy of an ideal gas • The internal energy of an ideal gas depends only on its temperature, not on its pressure or volume. • The temperature of an ideal gas does not change during a free expansion. PHY 2048, Dr. Hebin Li Heat capacities of an ideal gas CV is the molar heat capacity at constant volume. Cp is the molar heat capacity at constant pressure. The figure at the right shows how we could measure the two molar heat capacities. To produce the same temperature change, more heat is required at constant pressure than at constant volume. (∆𝑈 is the same) 𝐶𝑝 = 𝐶𝑉 + 𝑅 PHY 2048, Dr. Hebin Li