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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!
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.
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
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