Thermal Physics

Kinetic Theory Kinetic theory – all matter is made of small

particles (such as atoms, ions, or molecules) that are identical and in constant motion at a constant velocity.

All collisions between particles are “perfectly elastic” (meaning that the total amount of kinetic energy remains the same before and after the collision).

Temperature & Kinetic Energy The temperature of a substance is a

measurement of the average kinetic energy (energy of motion) of the molecules of that substance.

Kinetic energy = ½ (mass x velocity2) A decrease in kinetic energy = a decrease

in temperature because colder particles move more slowly and collide less.

Temperature Scales Celsius scale is based on freezing point (0

°C) and boiling point (100 °C) of water at sea level.

Kelvin scale is based on absolute zero (0 K) – the temperature at which all movement ceases (even electrons stop moving). Set up so that a change of 1 °C equals a change of 1 K, therefore the boiling point of water is 373 K.

K = °C + 273

Kinetic Theory & States of Matter Gas particles are far apart. They move randomly

around until they collide with another particle or the walls of their container. Thus, gases take the shape and volume of their container (indefinite shape and indefinite volume).

Liquid particles are closer together, but far enough apart that they can slip by each other. Thus, liquids take the shape of their container (indefinite shape and definite volume).

Kinetic Theory & States of Matter Although solid particles appear to stay in a fixed

position relative to each other, they are actually vibrating around a fixed point. Solid particles are packed closely together and can’t go far before they collide with another particle. Thus, solids have a definite shape and a definite volume.

At very high temperatures, collisions are so strong that e- are knocked away from atoms. This creates a gas-like state of e- and positive ions, called a plasma.

Kinetic Theory & States of Matter In terms of collisions, the most active state

of matter is: Plasma Gas Liquid Solid Bose-Einstein Condensate (BEC)

What is the Bose-Einstein Condensate?

New form of matter Based on Bose’s work,

predicted by Einstein 1st made in 1995 at CU

Boulder (Cornell & Wieman)

Scientists awarded 2001 Nobel prize in physics.

Forming a Bose-Einstein Condensate Lasers on all sides bombard

and slow down rubidium atoms.

Less movement = colder temperature

Magnetic field traps rubidium atoms by attraction with spinning electrons.

Hottest molecules allowed to escape.

Result: temperature = 170 billionths of a degree above absolute zero.

Properties of a Bose-Einstein Condensate

Behaves as one entity – a “superatom”. All atoms are identical. Atoms don’t have definite locations. Most atoms are in the same quantum level or

energy state. Similar to laser light in some respects.

Velocity distribution of Bose-Einstein condensate before (L) and during formation. The color corresponds to the number of atoms at each velocity. Lowest velocities appear blue and white.

Pressure Pressure (P) – the force per unit area on a surface. P = F/A P = pressure, measured in Pascals (1 Pa = 1 N/m2) F = force, measured in Newtons A = cross-sectional area, measured in m2

For a contained gas, pressure is the force of the molecules colliding with each other and the walls of the container.

Pressure example

How pressure is measured Pressure is measured using a barometer. How a barometer works Why a barometer uses mercury instead of

water, for example.

Pressure conversions Pressure can also be measured in mm Hg,

torr, or atmospheres (atm). 1 atm = 760 mm Hg 1 atm = 760 torr 1 atm = 1.013 x 10 5 Pa Conversion examples

What if there is more gas? More gas = more collisions = more

pressure A convenient way to measure # of

molecules is the mole. 1 mole of something = 6.02 x 1023

“somethings” For ex: 1 mole of eggs = 6.02 x 1023 eggs

Mole calculations 1 mole of a substance is the same mass (in grams)

as that of 1 atom or molecule of a substance (in amu).

Ex: 1 atom of carbon = 12 amu

1 mole of carbon = 12 g What would be the mass of 1 mole of CO2?

44 g 2 moles of CO2?

88 g

Ideal Gas Law The Ideal Gas Law demonstrates the

relationship between pressure, volume, temperature, and amount of substance for an ideal gas.

Ideal gas – a hypothetical gas that perfectly fits all the assumptions of the kinetic-molecular theory.

Noble gases show ideal behavior, but most other gases are real rather than ideal.

Ideal Gas Law Equation Ideal Gas Equation is PV = nRT P = pressure, measured in Pa. V = volume, measured in m3. n = number of moles of gas. R is the molar gas constant

= 8.31 J/(mol•K) T = temperature, measured in Kelvin.

PV diagrams Read and take notes on PV diagrams

(pages 84 – 85 in your textbook) HW: p 84: 15 - 19

Thermodynamics vocabulary

Thermodynamics – the study of energy relationships that involve heat, mechanical work, and other aspects of energy and energy transfer.

A thermodynamic system is a system that can interact and exchange energy with its surroundings in at least 2 ways, one of which is through heat transfer.

In thermodynamic equilibrium, heat transfer takes place so slowly that we can assume thermal equilibrium (temp remains uniform throughout the system), and volume changes so slowly that we can assume mechanical equilibrium (pressure remains uniform throughout the system).

Work done during volume changes

Let’s look at a piston of a car engine – it consists of a gas-filled cylinder with a movable piston (so volume can change). When the gas expands, it pushes with a force (F) against the cylinder moving it a distance (Δx), doing positive work.

W = F Δx but F = PA so W = PA Δx but A Δx = ΔVolume so W = P ΔV Where W = work (J) P = pressure (Pa) ΔV = change in volume (m3)

Work done during volume changes - 2

If the pressure remains constant: W = P (V2 – V1) If the pressure doesn’t remain constant (like

when an ideal gas is allowed to expand), then we have to add up all the products of each pressure and volume: W = P1ΔV1 + P2ΔV2 + etc

On a PV graph, the work would be equal to the area under the curve. Positive ΔV = positive work, negative ΔV = negative work.

1st Law of Thermodynamics

The internal energy of a system is the sum of all the kinetic and potential energies of its constituencies, symbolized by U.

1st Law of thermodynamics says that when heat Q is added to a system, some of the heat stays within the system, changing its internal energy by an amount ΔU. The rest of the heat leaves the system as work W. The equation is:

ΔU = Q – W Where ΔU = change in the internal energy of a system

(J) Q = heat added to the system (J) W = work done by the system (J)

1st Law of Thermodynamics – special case

If a system is cyclical (returns to its initial state), then ΔU = 0, and the 1st Law of Thermodynamics becomes:

Q = W for an isolated system The internal energy of an isolated system is

constant.

Thermodynamic processes An adiabatic process has no heat transfer in or out of a

system (Q =0). Achieved through insulation or quick transfer. ΔU = -W. For expansion, W is pos and ΔU is neg.

An isochoric process has a constant volume (W=0). Ex: heating a gas in a closed container. ΔU = Q.

An isobaric process has a constant pressure. Ex: Boiling water at room pressure. For an isobaric process: W = P(V2 – V1).

An isothermal process has a constant temperature. For an ideal gas in an isothermal process: ΔU = 0, and Q=W.

You should memorize these vocabulary terms!

Heat engine

A heat engine transforms heat partially into work or mechanical energy.

Matter inside the heat engine (the “working substance”) undergoes heat change, volume change, and sometimes a phase change.

For a gas engine, the working substance is fuel mixed with air. For a steam engine, the working substance is water.

Heat engine - reservoirs The hot reservoir gives the working substance heat at a

constant temperature TH. The heat transferred is QH. The cold reservoir absorbs heat from the working

substance at a constant temperature Tc. The heat transferred is Qc.

For a gas car, the burning fuel is the hot reservoir, and the environment is the cold reservoir.

Q is positive when it moves from the reservoir to the working substance, Q is negative when it moves from the working substance to a reservoir.

The useful output of the engine is the net work, W, done by the working substance.

Efficiency of a heat engine Thermal efficiency, e, of a heat engine is

given by the equation: e = W / QH

Where e = efficiency (unitless) W = useful work done by the engine (J) QH = heat transferred from the hot

reservoir (J) e is always less than 1, and can be

thought of as the fraction of heat that is put into work.

2nd Law of Thermodynamics The second law states that heat flows naturally

from regions of higher temperature to regions of lower temperature, but that it will not flow naturally the other way.

Heat can be made to flow from a colder region to a hotter region, which is exactly what happens in an air conditioner, but heat only does this when it is forced. On the other hand, heat flows from hot to cold spontaneously.

Due to friction, no heat engine can have 100 % efficiency.

Carnot’s principle How can an engine achieve its maximum

efficiency? It must operate using reversible processes in which

the system and the surroundings can be returned to the state they were in before the process began.

If energy is lost to friction during a process, the process is irreversible; if energy is lost as heat flows from a hot region to a cooler region, the process is irreversible.

Carnot's principle - The efficiency of an engine using irreversible processes can not be greater than the efficiency of an engine using reversible processes that is working between the same temperatures.

Carnot cycle stage 1 Stage 1: In the first stage,

the piston moves downward while the engine absorbs heat from the hot reservoir and gas begins to expand. The portion of the graph from point A to point B represents this behavior. Because the temperature of the gas does not change, this kind of expansion is called isothermic.

Carnot cycle – stage 2 Stage 2: In the second

stage, the heat source is removed; the piston continues to move downward and the gas is still expanding while cooling (lowering in temperature). It is presented by the graph from point B to point C. This stage is called an adiabatic process.

Carnot cycle – stage 3 Stage 3: The piston begins

to move upward and the cool gas is recompressed in the third stage. The heat goes to the cold reservoir. Point C - point D represents the decrease in volume and increase in pressure. The engine gives energy to the environment. This stage is an isothermal process.

Carnot cycle – stage 4 Stage 4: In the final stage,

the piston moves upward and the cool gas is secluded and compressed. Its temperature rises to its original state. Point D to point A illustrate this behavior; a continuing increase in pressure and decrease in volume to their initial position. It is an adiabatic process.

Entropy The second law can be restated in terms of

entropy, a measure of the disorder of a system.

Disorder means that the energy has been spread out within the system and is no longer available to do useful work.

The 2nd law can be restated as “in any thermodynamic process the total entropy always increases.”

Entropy equation For the change of entropy due to heat

added to a system: ΔS = Q/T ΔS is the change in entropy (in J/K) Q is the heat added to the system (in J) T is the temperature of the heat (in K)