Work and Heat Definitions

Transcription

1 Work and Heat Definitions FL- Surroundings: Everything outside system + q -q + System: he part of S the orld e are observing. Heat, q: transfer of energy resulting from a temperature difference Work, : transfer of energy as a result of unbalanced forces - Heat Sign convention: Positive heat is input to the system Negative heat is output from system Work Sign convention: Positive ork done on the system Negative ork done by the system

2 Expansion and compression FL-2 Figure 9. EXPANSION M h M OMPRESSION M Remove pins Remove pins h M Questions. What is system? Surroundings? 2. Ho does initial and final pressure correspond to P ext? 3. What is sign of ork for both cases? 4. Exactly ho much ork has been done?

3 EX-FL What if P ext is not constant? FL-3 If P ext is not constant during the expansion (or compression), the ork is the integral over the path from i to f and e need to kno ho P ext varies ith : = f P ext d i General expression. P ext is a function of.

4 Work is the area under P ext vs... FL-4 onsider an isothermal compression at constant pressure, P ext P f = P ext P f < P ext P f P f = P ext Δ = P ext Δ he curve is for an ideal gas, at constant : P = nr he ork is equal to the shaded area: note ho it depends on P ext. Figure 9.2

5 Reversible isothermal compression FL-5 Work depends on the path taken from to 2. For compression, the absolute minimum ork is done along the reversible path. Reversible path: At every infinitesimal step P ext is made infinitesimally larger than P. At every step, P ext is equal to the equilibrium gas pressure,. nr P gas = Figure 9.3 Is ork positive or negative?

6 Reversible isothermal expression EX-FL2 FL-6 Work depends on the path taken from to 2. For expansion, the absolute maximum ork is done on surroundings along the reversible path. = nr ln 2 rev (Ideal gas) Is ork positive or negative? Figure 9.3

7 State Functions vs Path Functions FL-7 As e ve seen, the ork depends on the path taken beteen initial and final state. Work and heat are path functions. State functions don t depend on the path taken but only upon the state of the system. Energy, U or H, are state functions. Why is this important??? he differentials of path functions are inexact and can t be integrated normally! he differentials of state functions are exact and can be integrated normally! State functions Path functions

8 he First La FL-8 he First La of hermodynamics: Energy is onserved. du q = δ + δ Differential Form ΔU = q + Integral Form Even though δq and δ are path functions (inexact differentials), their sum is a state function (exact differential).

9 Let s explore state vs. path more deeply! FL-9 3 reversible paths to the same place P,, P 2, 2, Path A: Reversible isothermal expansion Path B+: Reversible adiabatic expansion folloed by heating at constant volume Path D+E: Reversible constant-pressure expansion folloed by cooling at constant volume All three paths are reversible, but ill they all involve the same ork? ΔU?

10 Path A: Reversible Isothermal Expansion FL-0 A P,, P 2, 2, he energy of an ideal gas depends only on the temperature Recall U = (3/2)R du A = du = δ q + δ Since the process is reversible δ rev, A = Pgasd = nr d

11 Path B: Reversible Adiabatic Expansion FL- P,, P 3, 2, 2 Adiabatic: No energy transferred as heat. So q = 0. du = δ We can get from du B Recall from BZ/PFIG slides: Since ideal gas U depends only on : or Put it all together

12 Path : Heat at onstant FL-2 P 3, 2, 2 P 2, 2, onstant volume = NO P Work!! Δ U = qrev, + rev, = qrev, We need to find q rev, and ΔU q rev, = ΔU = 2 ( ) d From 2 to Path B + Path ΔU B + ΔU rev, B = ( ) d ( ) d = rev, = 2 ( ) d 0

13 Paths D and E Path D: onstant pressure expansion P,, P, 2, 3 D FL-3 E Path E: ooling at constant P, 2, 3 P 2, 2,

14 Path D + E FL-4 D E q rev rev = q + q = P ( ), D+ E rev, D rev, E 2 = + = P ( ), D+ E rev, D rev, E 2 Δ U = q + D + E = 0

15 Summary q,, ΔU FL-5 = P ( ) rev, D+ E 2 q rev, D+ E = 2 P ( ) Δ U rev +E, D = 0 q 2 rev, A = nr ln 2 rev, A = nr ln ΔU A = 0 = 2 rev, B+ ( ) d = qrev, B+ ( ) d Δ U rev, B+ = 0 ΔU, state function, is same for all paths but q rev and rev, path functions, differ based on path. 2