Thermodynamics Continues

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

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.

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

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

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

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

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

Looking further ….

PV/T = nR = constant !!! P1V1 = P2V2

T1 T2

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

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

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….

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.

Pressure Relationship

Due to the assumptions, pressure of a gas can be related to the behavior of the molecules themselves.

Kinetic Theory

KEavg = ½ mvavg2 = (3/2) kT

Solve for v vrms = √(v2)avg

vrms = (√3kT/m)

Kinetic Energy and Temperature ½ mv2 = KEavg= 3 /2 kT

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.

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)

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

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 ______