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
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