Example of a Spring Wind in Lubbock, Texas!

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

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

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

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

The Ch. 4 focus is on measurements of various macroscopic parameters: Work (W) Internal Energy (Ē) Heat (Q) Temperature (T) Entropy (S)

Sect. 4.1: Work (W) & Internal Energy (Ē) From Classical Mechanics, in principle, we know how to measure Macroscopic, Mechanical Work (W): Simply put, such a measurement would change an external parameter x of the system & observe the resulting change in the mean generalized force. (In what follows, Make the Replacement → X(x)). For a quasi-static, infinitesimal change, the infinitesimal work done is defined as: đW = X(x)dx.

For a quasi-static, infinitesimal change, the infinitesimal work done is defined as: đW = X(x)dx. Then, 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: x i → x f, where x i & x f are the initial & final x in the process. Of course, as we’ve discussed, The Work W Depends on the Process (depends on the path in the X – x plane!).

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

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

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 V 1 to V 2 is:

This clearly depends on the path taken. The work W done by the gas in expanding the cylinder from V 1 to V 2 is given by the integral: That is, the work W done is equal to the area of the region under the curve in a PV diagram.

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.

Note: There are many possible ways to take the gas from an 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!

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

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: p 1 = p 2 Isochoric Process  A process at constant volume, V 1 = V 2. Section 4.2: Heat (Q): The 1 st Law of Thermodynamics

More Thermodynamics Terminology I Isothermal Process  A process at constant temperature, T 1 = T 2 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.

The 1 st Law of Thermodynamics ΔĒ = Ē f – Ē i = Q – W For an infinitesimal, quasi-static process, this becomes dĒ = đQ - đW So, the mean internal energy Ē of a system tends to increase if energy is added as heat Q & tends to decrease if energy is lost as work W done by the system.

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

Temperature Triple Point of Water Constant Volume Gas Thermometer

p  Pressure in the gas, C  A constant. p 0  Atmospheric pressure ρ  Density of mercury in the Manometer p 3  Measured gas pressure

A gas thermometer temperature is

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