1. Ch. 4: Macroscopic Parameters & Measurement: Classical Thermo, Part I

2. Laws of Thermo: Overview
0th Law: Defines Temperature (T)
Allows the use of Thermometers!
1st Law: Defines Energy &
says total Energy is Conserved.
Also Defines
Internal Energy Ē, Heat Q,
& Mechanical Work W

3. They can not EVER be circumvented for such systems!
2nd Law: Defines Entropy (S)
3rd Law: Gives Entropy a
Numerical Value (as T  0!)
NOTE! These laws are
UNIVERSALLY VALID
for systems at equilibrium &
They can not EVER be circumvented for such systems!

4. Purely Macroscopic Physics Discussion The 4 Laws of Thermo!
Chapters 4 & 5:
In these chapters, we’ll have a
Purely Macroscopic
Physics Discussion
of the consequences of
The 4 Laws of Thermo!

5. Work (W) Internal Energy (Ē) Heat (Q) Temperature (T) Entropy (S)
Ch. 4 focuses on measurements of some macroscopic quantities:
Work (W)
Internal Energy (Ē)
Heat (Q)
Temperature (T)
Entropy (S)

6. Sect. 4.1: Work (W) & Internal Energy (Ē)
Classical Mechanics: Tells us, in principle, how to measure & calculate Macroscopic, Mechanical Work (W).
Simply put, a measurement or a calculation of W would change an external parameter x of the system & observe or calculate the resulting change in a mean generalized force <X>.

7. Make the replacement <X> → X(x).
Changing an external parameter x of the system allows the observation or calculation of the resulting change in a mean generalized force <X>. In what follows,
Make the replacement <X> → X(x).
For a quasi-static, infinitesimal change in x, the infinitesimal work done is defined as:
đW = X(x)dx.

8. W = ∫đW = ∫X(x)dx. đW = X(x)dx. The Work W Depends on the Process
For a quasi-static, infinitesimal change in x, the infinitesimal work done is:
đW = X(x)dx.
From the observed change in X(x) as a function of x, the macroscopic work done is the integral:
W = ∫đW = ∫X(x)dx.
Limits: xi → xf. xi & xf = initial & final x in the process.
Of course, as we’ve discussed,
The Work W Depends on the Process
(it depends on the path in the X – x plane!).

9. Example: Work Done by Pressure with a Quasi-static Volume Change Vi  Vf
The volume V is an external parameter.
So, the mean generalized force is the mean pressure <p> = p(V).
So, for a quasi-static volume change, the work done is the integral:
W = ∫đW = ∫p(V)dV
The limits are Vi → Vf.

10. W = ∫đW = ∫p(V)dV The Work W Depends on the Process
For a quasi-static volume change, the work done is:
W = ∫đW = ∫p(V)dV
The limits are Vi → Vf.
The Work W Depends
on the Process
That is, the work W depends on the path in the p – V plane!

11. So, the work W done by the gas in
Example
For a gas in a cylindrical
chamber with a piston,
The force on the piston is:
So, the work W done by the gas in
expanding the cylinder from V1 to V2 is:

12. This clearly depends on the path taken in the P-V plane!
The work W done by the gas in expanding
the cylinder from V1 to V2 is:
That is, the work W done is equal to the area
of the region under the curve in a PV diagram.
This clearly depends on the path taken in the P-V plane!

13. Question: If a gas is allowed to
complete a cycle, has net work been done?
The net work W done by
a gas in a complete cycle is
Equal to the Pink Area
of the region enclosed
by the path. If the cycle
is clockwise on the PV
diagram, the gas does
positive work.

14. many possible processes!
There are many possible ways to take the gas from
initial state i to final state f. The work done W is,
in general, different for each. This is consistent
with the fact that đW is an inexact differential!
Figures (a) & (b) are only 2 of the
many possible processes!

15. many possible processes!
Figures (c), (d), (e), (f) show 4 more of the
many possible processes!

16. The 1st Law of Thermodynamics Thermodynamics Terminology
Section 4.2: Heat (Q):
The 1st Law of Thermodynamics
Thermodynamics Terminology
Process  A change of a system from some initial macrostate to some final macrostate.
Path  The intermediate steps in a process between the initial & final macrostates.
Isobaric Process  A process at constant pressure: p1 = p2
Isochoric Process  A process at constant volume, V1 = V2.

17. More Terminology
Isothermal Process  A process at constant temperature, T1 = T2
Adiabatic Process  A process with
Q = 0 (No heat exchange)
Free Expansion Process  A process where Q = W = ΔĒ = 0
Cyclic Process  A process with the initial state = the final state.

18. 1st Law of Thermodynamics
ΔĒ = Ēf – Ēi = Q – W
For an infinitesimal, quasi-static process:
dĒ = đQ - đW
So, the mean internal energy Ē of a
system increases if energy is added
as heat Q & decreases if energy is
lost as work W done by the system.

19. Temperature, Temperature Scales (Ch. 3 Discussion Briefly Revisited!)
Section 4.3:
Temperature, Temperature Scales (Ch. 3 Discussion Briefly Revisited!)

20. Constant Volume Gas Thermometer
Temperature
Triple Point of Water
Constant Volume Gas Thermometer

21. Constant Volume Gas Thermometer
p  Pressure in the gas,
C  A constant.
p0  Atmospheric pressure
ρ  Density of mercury in the Manometer
p3  Measured gas pressure

22. A Gas Thermometer Temperature:

23. Celsius & Fahrenheit Scales
TC  Celsius Temperature.
T  Kelvin Temperature.
Conversion Between
Celsius & Fahrenheit: