thermodynamics continues. volume expansion Δv = βv 0 Δt where β is the coefficient of volume...
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Thermodynamics Continues
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Volume Expansion
ΔV = βV0 ΔT where β is the coefficient of volume expansion
Example: 4 liters of gasoline is heated from 20 C to 870C. How much is the volume of the gasoline increased?
Ans: 3.23 x10-4m3 or 323 L
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Water isn’t the only weird one!!! What does water have in common with Lead,
Uranium, Neon and Silicon? They all expand when they freeze. Other
elements contract. Water is at it’s highest density at 40C. Due to its hydrogen and crystal structure as it
freezes, ice is less dense than water.
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Boyle’s Law
Volume of a gas is inversely proportional to the pressure applied when kept at constant temperature.
V is proportional to 1/p
V1P1 = V2P2
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Charles Law
Volume of a gas is directly proportional the Temperature when kept at constant pressure.
V is proportional to T
V1 /T1 = V2 /T2
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Guy-Lussac’s Law
Pressure is proportional to Temperature when kept at constant Volume
P proportional to T at constant V
P1 / T1 = P2 / T2
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Ideal Gas Law PV = nRT
P Pressure Pa or N/m2 atm V Volume m3 L n moles mol mol R Universal Gas Constant
J/mol K L atm/mol K T Temperature K K
1 Pa = 1N/m2 1 atm = 1.013x105 Pa = 101.3 kPa
R = 8.315 J/mol K = .0821 L atm/mol K
Moles # of grams = to molecular mass
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STP
Standard Temperature and Pressure T = 273 K P = 1 atm = 101.3 kPa Example: What is the volume of one mole of
gas at STP? Ans: 22.4 L
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Looking further ….
PV/T = nR = constant !!! P1V1 = P2V2
T1 T2
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Try a problem
Example: A tire has 200 kPa of pressure at 100C. IF the tire heats to 400C, what is the pressure of the tire? (Hint assume no change in volume.)
Ans: 221 kPa
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Avagadro’s # and Boltzman’s Constant Avagadro’s number – NA = 6.02x1023
molecules per mole PV = NkT
Where N = number of molecules K = Boltzman’s Constant 1.38x10-23J/K = R/NA
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Kinetic Theory of Gases
Connection between what happens on the microscopic level and what we observed on the macroscopic level.
Imagine a gas made of a collection of molecules moving inside a container of volume V….
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Assumptions - Kinetic Theory of Gases Container holds a large #, N, of identical
molecules, each with a mass m and which behaves as a point particle;
Molecules move randomly in the container, obeying Newton’s Laws of motion at all times;
When molecules hit the walls or other molecules they behave in a perfectly elastic manner.
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Pressure Relationship
Due to the assumptions, pressure of a gas can be related to the behavior of the molecules themselves.
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Kinetic Theory
KEavg = ½ mvavg2 = (3/2) kT
Solve for v vrms = √(v2)avg
vrms = (√3kT/m)
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Kinetic Energy and Temperature ½ mv2 = KEavg= 3 /2 kT
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HEAT
Calorie – Heat needed to raise 1 g of water 10C Kilocalorie (Calorie) Heat needed to raise 1 kg
of water 10 C English Unit: BTU 1 kcal = 4186 J – Mechanical Equivalent of Heat Heat: Energy transferred from one thing to
another due to a difference in temperature.
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Heat vs. Thermal Energy
Heat: Energy Transfer
Thermal Energy: Internal Energy
U = 3/2 nRT U = Internal Energy
Q = mcΔT Q = Heat c = Specific Heat
Qlost= Q gained so… m1c1(Tf – T1)+ m2c2(Tf – T1) =0
or… m1c1(Tf – T1) = m2c2(T1 – Tf)
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Change of Phase
Heat of Fusion: Heat needed to take something from a solid to a liquid
Heat of Vaporization: Heat needed to take something from a liquid to a gas
Latent Heat (L): Heat values for heat of fusion or heat of vaporization
Q = mL m = mass L = latent heat
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Research and Present (Separately): 1st Law of Thermodynamics: Daniel
2nd Law of Thermodynamics: Molly Heat Death: Sarah Entropy: Megan, Andrew L. Carnot Cycle: Andy K. Heat Engines: Chris, Christine Heat Pumps and Refrigerators: Derek Conduction (Include R-value): Elizabeth, Tim Radiation and the Stefan-Boltzman Equation, Max
5 min max, Can discuss (don’t have to) with other person to avoid presenting duplication but each must research work individually and present individually. Due ______