p203/4c17:1 Chapter 17: The First Law of Thermodynamics Thermodynamic Systems Interact with surroundings Heat exchange Q = heat added to the system(watch sign!) Some other form of energy transfer Mechanical Work, e.g. W = done by the system (watch sign!) protosystem: ideal gas

p203/4c17:2 Work done during volume changes

p203/4c17:3 Isobaric Expansion expansion at constant pressure reversed => compression

p203/4c17:4 Isothermal Expansion (example 17-1) expansion at constant temperature reversed => compression

p203/4c17:5 Example: 1 m 3 of an ideal gas starting at 1 atm of pressure expands to twice its original volume by one of two processes: isobaric expansion or isothermal expansion. How much work is done in each case?

p203/4c17:6 Work Done Depends upon path!!!! A B

p203/4c17:7 Heat Transfer and “Heat Content” Two constant Temperature processes, same initial state slow expansion rapid expansion Final States (T, V and P) are the same Heat added in first process, not in second “Heat Content” not a valid concept

p203/4c17:8 Internal Energy U : Sum of microscopic kinetic and potential energies Changes in response to heat addition (Q) to the system Changes in response to Work done (W) by the system The First Law of Thermodynamics:  U = Q  W orQ =  U + W = Conservation of energy =>  U is independent of path! U is a function of the state of the system (function of the state variables). U = U(p,V,T) for an ideal gas. Infinitesimal processes dU = dQ - dW

p203/4c17:9 For an isolated system W = Q = 0  U = 0 U f =U i the internal energy of an isolated system is constant For a cyclic process system returns to its initial state state variables return to their initial values U f = U i => W net = Q net

p203/4c17:10 p 8.0 x 10 4 Pa 3.0 x 10 4 Pa 2.0 x m x m 3 a c b d Example: Thermodynamic processes not an ideal gas a-b 150 J of heat added b-d 600 J of heat added

p203/4c17:11 Thermodynamic Processes Isothermal: constant temperature generally dV  0 ; dW  0 ; dQ   Adiabatic: no heat transfer Q = 0 ; dQ = 0 Isochoric: constant volume (isovolumetric) dV = 0 => dW = 0 => Q =  U Isobaric: constant pressure dW = pdV => W = p  V Polytropic processes: one generalization, not (necessarily) iso- anything. pV r = const p V

p203/4c17:12 Internal Energy of an ideal gas. adiabatic free expansion Q = 0; W = 0 =>  U = 0  p  0 ;  V  0 ;  T = 0 => U depends upon T only Kinetic Theory U = sum of microscopic kinetic and potential energies each microscopic DOF averages 1/2 kT => U depends upon T only

p203/4c17:13 Molar Heat Capacities of Ideal Gases

p203/4c17:14 Constant pressure process: dQ = nC p dT = dU + dW vs dQ = nC p dT = dU for constant volume => C p > C V for any material which expands upon heating For an ideal gas:

p203/4c17:15 , another effective way of characterizing an ideal gas With the Equipartition Theorem

p203/4c17:16 Adiabatic Processes

p203/4c17:17 Adiabatic Processes (cont’d)

p203/4c17:18 Summary of basic thermodynamic processeses for an ideal gas

p203/4c17:19 Polytropic process for an ideal gas because not all processes are the basic types (iso*) or can be approximated by one of the basic process types polytropic exponent r pV r = const r = 0  > isobaric lim r  >  infinity  > constant volume r =   >  adiabatic r =1  >  isothermal