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

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

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!

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!

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)

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>.

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.

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!).

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.

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!

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:

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!

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.

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!

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

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.

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.

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.

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

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

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

A Gas Thermometer Temperature:

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