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( 0 F) = 9/5T( 0 C) + 32 Celsius (centigrade) T( 0 C ) = 5/9[T( 0 F) –32] (degree is 9/5 that of Fahrenheit) Kelvin (Celsius + 273)

Examples Zero degrees Celsius is what Kelvin? Answer: 273 o What is the boiling point of water in degrees Kelvin? Answer: 373 o 200 degrees Celsius is what in Kelvin? Answer: 473 o

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 A B C

Thermal Expansion Nearly all substances expand when heated and contract when cooled Exception- water below 4 0 C For solids change in length is proportional to length and change in temperature  L =  L 0  T  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 An aluminum beam 3.0 m in length is heated from 20 0 C to 80 0 C. What is the increase in length?  L =  L 0  T = 25 x x 3.0 x 60 = 4.5 x 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 as  T (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 = J/(mol K) or (L atm)/(mol K) Pressure in Pascals (Pa) or atmospheres 1 atm = x 10 5 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 (20 0 C). What is the absolute pressure(in Pa and atm)? P = nRT/V = J/(mol K) ( ) /10 -3 m 3 = 2.4 x 10 6 N/m 2 = 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? H 2 O 2 H 2 O CO 2 He

Volume of One Mole at STP Standard temp = 0 0 C = K Standard P = 1.00 atm = x 10 5 N/m 2 V = nRT/P = (1.00 mol)(8.315 J/molK)(273 K) (1.013 x 10 5 N/m 2 ) = 22.4 x m 3 = 22.4 liters Remember: 10 3 liters = 1 cubic meter Use degrees Kelvin (Celsius + 273)

Another Example A 200 liter tank contains hydrogen gas at room temperature (20 0 C) and absolute pressure of 5 atmospheres. How many moles and grams of hydrogen are in the tank? Hint n = PV/RT 5atm x x 10 5 Pa x 200 x / / 293 = 41.6 moles = 83 grams

Alternate form of Ideal Gas Law P 1 V 1 /T 1 = P 2 V 2 /T 2 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 N A = Avogadro’s number = number of molecules in a mole = 6.02 x mol -1 k = R/N A = Boltzmann’s constant = 1.38 x J/K = gas constant per molecule N/N A = 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 KE av = ½ m (v 2 ) = (3/2) kT –k is Boltzmann’s constant = 1.38 x J/K v rms = ( 3kT/m) 1/2 not equal to v av 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? v rms 2 = 3 x 1.38x x 293 / (32 x 1.67 x ) v rms = 480 m/s 1 amu = 1.66 x kg proton mass = 1.67 x kg

Distribution of Molecular Speeds Courtesy Hyperphysics, Georgia State University

Kinetic Theory Simulations astr.gsu.edu/hbase/kinetic/kintem.htmlhttp://hyperphysics.phy- astr.gsu.edu/hbase/kinetic/kintem.html