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Chapter 17

Chapter 17. The First Law of Thermodynamics. Thermodynamic Concepts. Thermodynamic system: able to exchange heat with its surroundings State variables: p , V , T , ... describe the thermodynamic system Thermodynamic process: changes the state ( p , V , T , ...) of the system.

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Chapter 17

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  1. Chapter 17 The First Law of Thermodynamics

  2. Thermodynamic Concepts • Thermodynamic system:able to exchange heat with its surroundings • State variables: p, V, T, ...describe the thermodynamic system • Thermodynamic process:changes the state ( p, V, T, ...) of the system

  3. Thermodynamic Process Heat Q: can leave or enter system Work W: • system can do work on its surroundings • surroundings can do work on the system

  4. thermodynamicsystem:can exchange heat with its surroundings state of system:(p, V, T, ...) thermodynamicprocess:changes state of the system

  5. thermodynamicprocess:changes state of the system We’ll focus on the roles of: • Heat Q • Work W

  6. Heat Q:can leave or enter system Q > 0: heat added to system Q < 0: heat removed from system

  7. Sign Conventions for Q Q > 0: heat added to system Q < 0: heat removed from system • Consistent with sign of DT from earlier: Q = mc DT or Q = nC DT

  8. Work W: W > 0: system does work on its surroundings W < 0: surroundings does work on the system

  9. Sign Conventions for W W > 0: system does work on surroundings W < 0: surroundings does work on system • (the ‘opposite perspective’ as in mechanics)

  10. (a) Q > 0, W = 0 (b) Q < 0, W = 0 (c) Q = 0, W > 0 (d) Q = 0, W < 0 (e) Q > 0, W > 0 (f) Q < 0, W < 0

  11. Work done when volume changes

  12. Work done when volume changes

  13. Work done when volume changes

  14. Work W is path-dependent • W = area under graph of the function p(V) • W depends on initial and final states (1, 2) • W depends on path taken (intermediate states)

  15. Q (= heat transferred) is also path-dependent

  16. Thermodynamic Concepts • Thermodynamic system:described by state variables (p, V, T, ..) • Thermodynamic process:changes the state ( p, V, T, ...) of the system • Heat Q, Work W:‘path-dependent’: values depend on process

  17. Heat Q and Work W • Q and W are not properties of the system (Q enters or leaves the system) (W is done on or by the system) • We can measure the difference: Q – W • Q – W is related to a property of the system

  18. Q – W • We choose a thermodynamic system • We take the system between a fixed initial final state for many different processes • For each process, we measure Q – W • Experiment surprises us!

  19. Q – W • For this setup, we always find: • Q – W has same value for all processes • Q – W depends only on initial, final state • Q – W is path-independent (these are three equivalent statements)

  20. Q – W Since Q – W depends only on state variables: Q – W = a change in a property of the system We define U = ‘internal energy’ of system: Q – W = DU

  21. First Law of Thermodynamics Q – W = DU or Q = W + DU • Generalizes conservation of energy from just mechanical energy to include heat energy

  22. First Law of Thermodynamics Q – W = DU or Q = W + DU • The heat energy Q added to a system goes into work W and change in internal energy U

  23. First Law of Thermodynamics Q – W = DU or Q = W + DU • (Notation: U is not simply ‘potential energy’)

  24. Laws of Thermodynamics Zeroth Law: ‘every thermodynamic system has a property called temperature T’ First Law:DU = Q – W ‘every thermodynamic system has a property called internal energy U’

  25. DU = Q – W Recall: • Q can be > 0, < 0, = 0 • W can be > 0, < 0, = 0 Thus: • DU can be > 0, < 0, = 0

  26. Free Expansion • Break partition • Let gas expand freely into vacuum

  27. Free Expansion • gas is in equilibrium at initial and final states • gas is not in equilibrium between initial and final states

  28. Free Expansion • Set-up for process: Q = 0 (insulation)W = 0 (no pushing) • First Law says:DU = Q – W = 0

  29. Free Expansion • For the gas:Dp , DV are nonzero • Experiment shows: • low density (‘ideal’) gases have DT = 0 between initial and final states

  30. Free Expansion • For the gas:Dp , DV are nonzero • Experiment: DT = 0 • First Law: DU = 0 • Conclude: For an ideal gas, U only depends on T

  31. Laws of Thermodynamics Zeroth Law: ‘every thermodynamic system has a property called temperature T’ First Law:DU = Q – W ‘every thermodynamic system has a property called internal energy U’

  32. First Law of Thermodynamics Q – W = DU or Q = W + DU • Generalizes conservation of energy: • Heat energy Q added to a system goes into both work W and change in internal energy U

  33. Thermodynamic Processes Process Definition Consequence Free Expansion: Q = 0 W = 0 DU = 0 Cyclic: closed loop DU = 0 Q = 0 + W

  34. Thermodynamic Processes Process Definition Consequence Isobaric p = constant W = p DV Isochoric V = constant W = 0 Q = DU + 0

  35. Thermodynamic Processes Process Definition Consequence Isothermal T = constant DU = 0 (must be slow) Adiabatic Q = 0 0 = DU + W (insulated or fast)

  36. Molar Heat Capacity Revisited Q = n CDT • Q = energy needed to heat/cool n moles by DT • CV = molar heat capacity at constant volume • Cp = molar heat capacity at constant pressure

  37. Molecular Theory: (Ktot)av = (f/2) nRT CV= (f/2)R Monatomic: f = 3 Diatomic: f = 3, 5, 7 New language: U = (f/2) nRT CV= (f/2)R Monatomic: f = 3 Diatomic: f = 3, 5, 7 CVfor Ideal Gases, Revisited

  38. Cpfor Ideal Gases • We expect: Cp > CV • Example: gas does work expanding against atmosphere • We can show: Cp = CV + R Derive this result

  39. Cpfor Ideal Gases • monatomic gas:CV = (3/2)R • diatomic gas: at low T, CV = (5/2)R

  40. Adiabatic Process (Q = 0) • An adiabatic process for an ideal gas obeys: TV g -1 = constant value pV g = another constant Derive these results

  41. Adiabatic Process (Q = 0) For an ideal gas undergoing an adiabatic process: Derive these results Derive some isobaric results Do Problem 17-42

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