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

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

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 = °C Fahrenheit scale – zero = lowest achievable temperature in lab ● 96 °F = body temperature ● Currently: boiling = 212 °F, freezing = 32 °F

● To convert between temps, consider a linear relation between them: T F = aT c + b ● To determine a & b, use equivalent temps. ● First freezing

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

● 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

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

ΔT K = ΔT C ➔ T K = T C ● Absolute temperature scale must be used when no change in temperature

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

Linear Expansion – Cont. ● Exp: ΔL α L 0 (original length) ● Constant to create equality: α = coefficient of linear expansion ● Unit: °C -1 ➔ ΔL = α L 0 ΔT ● α is experimentally determined

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

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

● 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

● 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

Area Expansion ● Area must expand as well ● Consider a square, side L

Volume Expansion ● Does a cutout hole become larger or smaller when heated ● Using similar process ➔ ΔV = β V 0 ΔT 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

Expansion of Water ● Most notable exception: water ● Most dense at 3.98 °C as liquid

● 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

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

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)

● 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

Ideal Gas Law – Cont. ● k = Boltzmann Constant ● k = 1.38 x J/K ● A fundamental Constant of Nature ● Creates: Ideal Gas Law ➔ P V = N k T

● 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 molecules = N A ● N A = avogadro’s number

➔ N = n N A ● Substituting: ● P V = n N A k T ● N A k = constant = Ideal Gas Constant, R ● R = 8.31 J / mol K ● P V = n R T

● 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 / N A ● M is determined by the periodic table

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

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