1. The First Law of Thermodynamics
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. Q > 0: heat added to system
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 = 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 = Q = DU + 0

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

36. Molar Heat Capacity Revisited
Q = n C DT
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. CV for Ideal Gases, Revisited
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

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

39. Cp for 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