Heat and Temperature

Matter is made of Atoms

Electron Microscope Photo of Germanium Atoms

Atoms are in Constant Motion

Temperature

• Measure of how hot or cold an object is

• Measured by thermometers

• Work by expansion of a liquid

• Other types use bimetallic strip

Temperature Scales

• Fahrenheit T(0F) = 9/5T(0C) + 32

• Celsius (centigrade) T(0C ) = 5/9[T(0F) –32]

(degree is 9/5 that of Fahrenheit)

• Kelvin (Celsius + 273)

Examples

• Zero degrees Celsius is what Kelvin?

Answer: 273o

• What is the boiling point of water in degrees Kelvin?

Answer: 373o

• 200 degrees Celsius is what in Kelvin?

Answer: 473o

Zeroth Law of Thermodynamics

• If two systems are in thermal equilibrium with a third system, they are in thermal equilibrium with each other

• Thermal equilibrium occurs when objects in contact are at same temperature and no energy flows between them

AB C

Thermal Expansion

• Nearly all substances expand when heated and contract when cooled

• Exception- water below 4 0C• For solids change in length is proportional

to length and change in temperature• L = L0T is coefficient of linear expansion,

different for different substances

Metals Expand the Most

• In solid object all sections expand with increased temperature

• Aluminum expands more than iron or brass• Engine pistons are made of aluminum,

cylinders of iron• Overheating engine ruins (scuffs) piston• Bridge and sidewalk sections must be spaced

Expansion Example

• Aluminum has a coefficient of linear expansion of 25 x 10-6 An aluminum beam 3.0 m in length is heated from 200C to 800C. What is the increase in length?

L = L0T =

25 x 10-6 x 3.0 x 60 = 4.5 x 10-3 m = 4.5 mm

Bi-metallic Strip demo

Ideal Gases

• When pressure is less than 1 atm and gas is not near liquifaction temperature

V goes as/p (inverse proportion)

V goes asT (direct proportion)

Gay-Lussac’s Law

• At constant volume, the pressure of a gas is proportional to the absolute (Kelvin) temperature

• Example: What would happen if you throw a closed aerosol can into a fire?

Ideal Gas Law

• Combines laws of Boyle, Charles and Gay-Lussac• PV = nRT (equation of state for ideal gas)• n = number of moles of gas• R is gas constant = 8.315 J/(mol K)

or 0.0821 (L atm)/(mol K)• Pressure in Pascals (Pa) or atmospheres• 1 atm = 1.013 x 105 Pa

PV = nRT• Memorize

• Make sure you understand what P, V, n, R, and T are

Example

• One mole of hydrogen fills a pressure bottle one liter in volume at room temperature (200 C). What is the absolute pressure(in Pa and atm)?

P = nRT/V =

8.315 J/(mol K) (273 + 20) /10-3 m3 =

2.4 x 106 N/m2 = 24 atm

Mole

• Amount of substance that contains as many atoms or molecules as there are in 12 grams of Carbon 12

• That number of grams of a substance numerically equal to the molecular mass of the substance

What is the Molecular Mass?

• How many grams per mole?

• H2

• O2

• H2O

• CO2

• He

Volume of One Mole at STP

• Standard temp = 00C = 273 0K• Standard P = 1.00 atm = 1.013 x 105 N/m2

• V = nRT/P = (1.00 mol)(8.315 J/molK)(273 K)

(1.013 x 105 N/m2)

= 22.4 x 10-3 m3 = 22.4 liters

Remember: 103 liters = 1 cubic meter

Use degrees Kelvin (Celsius + 273)

Another Example

• A 200 liter tank contains hydrogen gas at room temperature (200 C) and absolute pressure of 5 atmospheres. How many moles and grams of hydrogen are in the tank?

• Hint n = PV/RT

5atm x 1.013 x 105 Pa x 200 x 10-3 / 8.315 / 293 = 41.6 moles = 83 grams

Alternate form of Ideal Gas Law

• P1V1/T1 = P2V2/T2

• Use to solve problems where one of these six variables is unknown

• Isolate that one and

plug in given information

Ideal Gas Law in Terms of Molecules

• PV = NkT = nRT• N = number of molecules in sample• NA = Avogadro’s number = number of

molecules in a mole = 6.02 x 1023 mol-1

• k = R/NA = Boltzmann’s constant = 1.38 x 10-23 J/K = gas constant per

molecule

N/NA = n

Nk = nR• Memorize and know how to derive

Assumptions of Kinetic Theory

• In ideal gas large numbers of molecules move with varying speeds in random directions

• Average molecules are much further apart than their size

• Molecules interact only when they collide

• Collisions are assumed perfectly elastic

Molecules in a Box

Consequences of Kinetic Theory

• The average translational kinetic energy of molecules in a gas is proportional to the absolute temperature

• KEav = ½ m (v2 ) = (3/2) kT– k is Boltzmann’s constant = 1.38 x 10-23 J/K

• vrms = ( 3kT/m)1/2 not equal to vav

Question: If you double the rms speed of molecules in a gas, what happens to the temperature?

Example

• What is the rms speed of an oxygen molecule at room temperature?

vrms2 = 3 x 1.38x 10-23 x 293 / (32 x 1.67 x 10-27)

vrms = 480 m/s

1 amu = 1.66 x 10-27 kg proton mass = 1.67 x 10-27 kg

Distribution of Molecular Speeds

Courtesy Hyperphysics, Georgia State University

Kinetic Theory Simulations

• http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/kintem.html