TEMPERATURE & ZEROTH LAW OF THERMODYNAMICS

1. TEMPERATURE & ZEROTH LAW OF THERMODYNAMICS Heat – transfer of energy due to temperature differences • Heat flows - objects do not have heat • Heat flows due to thermal contact • Energy is transferred until temperatures are the same = they are in thermal equilibrium

2. Thermal Equilibrium • Thermal contact is not necessarily physical contact – think warming by fire • Heat flows from hot object to cool one • Nothing to do with type of material or energy content • Zeroth Law – all objects in thermal equilibrium with one another have same temperature • Think thermometers

3. TEMPERATURE Celsius scale – based on boiling/freezing point of water (at sea level) • 100 °C & 0 °C • Zero level for any scale is arbitrary • No upper limit, lower limit = -273.15 °C Fahrenheit scale – zero = lowest achievable temperature in lab • 96 °F = body temperature • Currently: boiling = 212 °F, freezing = 32 °F

4. To convert between temps, consider a linear relation between them: TF = aTc + b • To determine a & b, use equivalent temps. • First freezing

5. Absolute Zero • Temperature at which heat energy cannot be extracted • Called 0 kelvin, 0 K • On kelvin temp scale – no negative temps • Increments of temp same as celsius

6. Absolute Zero is not attainable experimentally, must extrapolated from graph • Use a gas thermometer • As gas is cooled, the volume , as does the pressure • Temperature, Pressure/Volume create a linear relationship

7. Absolute Zero is an extrapolation of this linear relationship • The temperature intercept is the same regardless of the gas used

8. ΔTK = ΔTC  TK = TC + 273.15 • Absolute temperature scale must be used when no change in temperature

9. THERMAL EXPANSION • Most substances expand when heated • One dimensional • Experiments have found Δlength (of rod) αΔT • Causes atoms to vibrate more actively & with greater amplitude • Therefore they move further apart & object expands • Expansion is quite small

10. Linear Expansion – Cont. • Exp: ΔL α L0 (original length) • Constant to create equality: α = coefficient of linear expansion • Unit: °C-1  ΔL = α L0ΔT • α is experimentally determined

11. Linear Expansion – Cont. • Most materials, α is positive • Some with very strong atomic bonding (ceramics) are close to zero or negative • This creates a need for expansion gaps in bridges, roads & sidewalks

13. Bimetallic Strips • Two metals with different expansion coefficients • Always bends towards side with smaller coefficient • Used in thermostats, circuit breakers, thermometers

14. Atomic theory is incomplete – we cannot write out equation at atomic level • Can only describe macroscopically – in terms of measurable quantities • Interatomic bonding determines: melting temperature & expansion • Inversely related to one another • High melting temp = low thermal expansion • Sn & Si do not fall on line do to relatively strong covalent (shared) bonding

15. Thermal expansion equation is useful, but not a fundamental eqn. • α increases with  temperature and in practice require extensive modifications • Some materials expand differently depending on direction • In reality, nature is more complicated than it appears

16. Area Expansion • Area must expand as well • Consider a square, side L

17. Volume Expansion • Does a cutout hole become larger or smaller when heated • Using similar process  ΔV = β V0ΔT β = coefficient of volume expansion • The weak intermolecular bonds cause β ~ 3 α • Holes expand with heating • Objects expand the same whether solid or hollow

18. Expansion of Water • Most notable exception: water • Most dense at 3.98 °C as liquid

19. Cold lakes must be uniform 3.98 • Before any freezing can occur • Lakes freeze from top down • Deep lakes are not cold long enough to completely freeze • Frozen layer at surface act as an insulator • Other materials: bismuth, antimony & cast iron

20. THE IDEAL GAS LAW • Since gases expand to fill container, there is not a simple temperature dependent volume change • Basic relationship were discovered experimentally • Recall: Pressure of constant volume of gas varies linearly with temperature

21. The Ideal Gas Law – Cont. • As temperature , eventually the gas liquifies – this is due to molecular interactions • An ideal gas, the molecular interactions are so small it never becomes a liquid • Consider: Describe pressure, P, of an ideal gas based on: T, number of molecules, N, and V • P α N when T & V constant (inflation)

22. P α T when N & V constant • P α 1 / V when T & N constant (compression) • Combining: P α N T / V • Need to determine constant

23. Ideal Gas Law – Cont. • k = Boltzmann Constant • k = 1.38 x 10-23 J/K • A fundamental Constant of Nature • Creates: Ideal Gas Law  P V = N k T

24. A relationship between thermal properties of a substance – equation of state • This can also be written in terms of a mole (mol) • A quantity of something • Usually molecules (based on carbon) • Variable: n • 1 mole = 6.02 x 1023 molecules = NA • NA = avogadro’s number

26.  N = n NA • Substituting: • P V = n NA k T • NA k = constant = Ideal Gas Constant, R • R = 8.31 J / mol K • P V = n R T

27. 1 mol of anything has the same number of particles • What differs is the mass of the mol • Define atomic or molecular mass, M as mass / mol  m = M / NA • M is determined by the periodic table

28. KINETIC THEORY OF GASES • Behavior at the atomic scale • Pressure is a consequence of collisions of molecules with walls of container

29. Kinetic Theory – Cont. • To show this, we assume the following: • The # of molecules is large & average separation between them is large (container is mostly empty space) • Molecules