Example of a Spring Wind in Lubbock, Texas!

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

Laws of Thermodynamics: Overview

• 0th Law: Defines Temperature (T) Allows the use of Thermometers!

• 1st Law: Defines Energy & Says Energy is Conserved.

Also Defines • Internal Energy Ē• Heat Q• Mechanical Work W

• 2nd Law: Defines Entropy (S) • 3rd Law: Gives Entropy a

Numerical Value (at low T!) • NOTE! These laws are

UNIVERSALLY VALIDfor 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 <X>. (In what follows, Make the Replacement <X> → 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: xi → xf, where xi & xf 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 Vi Vf

• If the volume V is the external parameter, 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)dVThe limits are Vi → Vf.

• For a quasi-static volume change, the work done is the integral:

W = ∫đW = ∫p(V)dVThe limits are Vi → Vf.

The Work W Depends on the Process

(depends on the path in the p – V plane!)

A

dVP

dxF

dx

dWF PA

PAdxdW PdV

2

112

V

VPdVW

Example•For a gas in a cylindricalchamber with a piston, The force on the piston is:

•So, the work W done by the gas inexpanding the cylinder from V1 to V2 is:

1Vo

P

V2V

'11

2

This clearly depends on the path taken.

•The work W done by the gas in expanding thecylinder from V1 to V2 is given by the integral:

2

112

V

VPdVW

•That is, the work W done is equal to the area of theregion under the curve in a PV diagram.

o

P

V

2

1

2V1V

•Question: If a gas is allowed to complete acycle, has net work been done?

•The net work W done by agas in a complete cycle is

Equal to the Pink Area of the region enclosed bythe path. If the cycle isclockwise on the PVdiagram, the gas doespositive 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 themany possible processes!

Figures (c), (d), (e), (f) are 4 more of themany 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: p1 = p2

• Isochoric Process A process at constant volume, V1 = V2.

Section 4.2: Heat (Q): The 1st Law of Thermodynamics

More Thermodynamics TerminologyI

• 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.

The 1st Law of Thermodynamics

ΔĒ = Ēf – Ēi = Q – W• For an infinitesimal, quasi-static process,

this becomes

dĒ = đQ - đW•So, the mean internal energy Ē of a systemtends to increase if energy is added as heatQ & tends to decrease if energy is lost aswork W done by the system.

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

TemperatureTriple Point of Water

erature)point temp-(triple 16.2733 KT

Constant Volume Gas

Thermometer

CpT

Constant Volume Gas Thermometer

CpT

ghpp 0

p Pressure in the gas,C A constant.p0 Atmospheric pressureρ Density of mercury in the Manometerp3 Measured gas pressure

33 CpT

A gas thermometer temperature is

)lim)(16.273(3

0 p

pKT

gas

al)(provision ))(16.273()(33

3 p

pK

p

pTT

Celsius & Fahrenheit Scales

Conversion Between Celsius & Fahrenheit:

TC Celsius Temperature.T Kelvin Temperature.

015.273TTC

FC 00 320

00 95 FC 032

5

9 CF TT