Thermal Physics : Thermodynamics

Dr Stuart Reid [email protected] Royal Society of Edinburgh/Scottish Government Research Fellow room 461

8+1 lectures

Objectives (from Course Guide 2008/09) Y&F ch: 1. Temperature and Heat (3 lectures) a. Temperature and Thermal Equilibrium b. Zeroth law of thermodynamics c. Thermometric properties 17.1‐3 d. Thermal expansion of liquids and solids 17.4 e. Specific Heat Capacity f. Calorimetry and Phase Changes 17.5‐6 2. Mechanisms of Heat Transfer (2 lectures) a. Conduction b. Convection 17.7 c. Radiation, Stefan‐Boltzmann law, black body 3. Equations of state ‐ Ideal and Real Gases (2 lectures) a. Equations of state; ideal gas equation b. Van der Waals equation 18.1‐2 c. pV diagrams, phase of matter

Examples of typical applications: 1. Need for different kinds of thermometer (industrial, medical, etc.); expansion joints in bridges 2. Heat sinks for ICs; double glazing; insulation; thermal boxes; sea breezes; sunbathing

Einstein’s thoughts: “A theory is the more impressive the greater the simplicity of its premises, the more varied the kinds of things it relates and the more extended the area of its applicability. Therefore classical thermodynamics has made a deep impression upon me. It is the only physical theory of universal content which I am convinced, within the areas of the applicability of its basic concepts, will never be overthrown.”

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Thermodynamics was one of William Thomson’s (Lord Kelvin’s) legacies.

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1. Temperature and Heat (17.1‐6)

How to think: • Identify variables in a problem • Define the apparatus (the system)

‐ A system is enclosed by boundaries ‐ The rest “out there” is called the surroundings ‐ STATE: described by some variables called “STATE VARIABLES”

Goal: to reduce problems to as few variables as possible.

Examples: Dynamics: e.g. billiard balls → n balls, m, v, x, y Electricity: e.g. circuit → electrons, V, I, R Thermodynamics: cylinder & pistons → n atoms, m, P, V, T *** Things change with temperature – banana to 77 K demo ***

What is temperature? The temperature of a system is proportional to the average kinetic energy of the atoms or molecules.

Thermal Equilibrium Two systems are at thermal equilibrium when they are at the same temperature. Generally the systems are different; all they share in common is the same temperature.

Examples: Glass of cold water left in the room → approaches thermal equilibrium Microprocessor and a cold block of Al

T1 T2 thermal contact

Suppose we have a third system: e.g. the table that the glass of water is on 1 2 3 If T1 = T2 T1 T2 T3 and T2 = T3 then T1 = T3 This is the 0th law of thermodynamics – “If two thermodynamic systems are in thermal equilibrium with a third, they are also in thermal equilibrium with each other.”

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Temperature Scales

• We need reference points • We need something that varies with temperature ‐ and we need to know how it varies, ideally linearly!

END LECTURE 1 (1) Reference Points

a) Boiling water 100˚C (Celcius/Centigrade) Ice 0˚C b) Human body Fahrenheit “96” Freezing point of water “32” Coldest solution possible (water + ice+ salt) “0” c) Triple point: at the exact pressure and temperature, the combination of pure water, pure ice and pure vapour can coexist in a stable equilibrium

Boiling

Freezing

NB. In space, where the temperature approaches close to absolute zero, ice when heated will convert directly to vapour/steam without any liquid‐phase.

Triple Point = 273.16 K

Absolute zero → no molecular motion → 0 K

To convert: T (˚C) = T (K) – 273.15

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Measuring temperature

• Change in electrical resistance (convenient but not very linear) • Change in length of a bar (bimetallic strip) • Change in volume of a liquid • Change in volume of gas (very accurate but slow and bulky)

Thermal Expansion “ Hotter things become longer”

• In general, most materials expand upon being heated (but not water where between 0°C ‐> 4°C it gets smaller! Also many rubbers contract on heating).

Linear thermal expansion: ΔL = αL0ΔT *

• where α is “coefficient of linear expansion”

• definition of but can be approximate at one temperature T for small changes in temperature as shown in equation above (*).

Examples

A 1 metre long bar heated by 1 degree gets bigger by: Steel ≈0.01 mm Glass ≈ 0.001 mm Zerodur ≈ 0.0001mm Rails expand and may buckle on a hot summer day

Join two metals with different coefficient of thermal expansion:

e.g. fire alarm

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Hotter things take up more volume Thermometer relies on a thermal expansion of a liquid (e.g.mercury)

Thin tube (Gives big length change for

small increase in volume)

Large volume of reservoir

Example The markings on a steel ruler are made at 30˚C in a hot factory. Assuming the ruler is perfectly precise, how inaccurate will the ruler become at measuring 30 cm across a ‐5 ‐1 sheet of ice at 0˚C? αsteel = 1.2×10 ˚C .

Ans:

ΔL = αL0ΔT ΔL = 1.2×10‐5 ˚C‐1 × 0.3 m × 30 ˚C = 1.08 ×10‐4 m ≈ 100 μm or 0.1 mm

Example 2 Rail tracks: If a gap is placed every 100 m to compensate for thermal expansion, how large would the gap have to be? The temperature can range from ‐10˚C to + 30˚C. ‐5 ‐1 The track was laid at 10˚C. Again αsteel = 1.2×10 ˚C .

Ans: want gap = 0 m when temperature at maximum (30˚C)

ΔL = αL0ΔT = 1.2×10‐5 ˚C‐1 × 100 m × 20 ˚C = 0.024 m = 2.4 cm

Δ β Δ Volume thermal expansion: V = V0 T where β = coefficient of volume expansion K‐1 or ˚C‐1.

(sometimes written as αv in other sources)

NB. Both α and β vary somewhat with temperature and therefore these equations are approximations and only valid for small temperature changes.

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Relating α to β (linear to volume expansion)

Consider a cube of solid material: L

V = L3 L

L

At initial temperature, we have the values L0 and V0.

As the temperature increases by dT, each length will likewise increase by dL, and the volume increases as dV, such that:

since

We can replace L and V in terms of their initial values L0 and V0 since we know:

†

3 And since V0=L , we can write dV as:

subs in †

This is only consistent with dV = βV0dT only if

See Y&F ch.17.1 and can check against table values for α and β.

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*** Things change with temperature – Al sheet with ball bearing demo ***

DISTANCES: between any two points increases during expansion. i.e. hole get bigger!

Y&F illustration:

NOT THIS!

YES!

END LECTURE 2

Reason for expansion (microscopic)

r

• Potential energy of two atoms • Vibrate in an asymmetric potential well

As T increase, energy increase → average position increases

U(r) average separation

r thermal High T excitation Low T (P.E.)

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