Thermodynamics Continues

Volume Expansion ΔV = βV 0 ΔT where β is the coefficient of volume expansion Example: 4 liters of gasoline is heated from 2 0 C to 87 0 C. How much is the volume of the gasoline increased? Ans: 3.23 x10 -4 m 3 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 4 0 C. 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 V 1 P 1 = V 2 P 2

Charles Law Volume of a gas is directly proportional the Temperature when kept at constant pressure. V is proportional to T V 1 /T 1 = V 2 /T 2

Guy-Lussac’s Law Pressure is proportional to Temperature when kept at constant Volume P proportional to T at constant V P 1 / T 1 = P 2 / T 2

Ideal Gas Law PV = nRT  P PressurePa or N/m 2 atm  VVolumem 3 L  nmolesmolmol  RUniversal Gas Constant J/mol KL atm/mol K  TTemperature KK 1 Pa = 1N/m 2 1 atm = 1.013x10 5 Pa = kPa R = 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 = kPa Example: What is the volume of one mole of gas at STP? Ans: 22.4 L

Looking further …. PV/T = nR = constant !!! P 1 V 1 = P 2 V 2 T 1 T 2

Try a problem Example: A tire has 200 kPa of pressure at 10 0 C. IF the tire heats to 40 0 C, 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 – N A = 6.02x10 23 molecules per mole PV = NkT  Where N = number of molecules  K = Boltzman’s Constant 1.38x J/K = R/N A

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 KE avg = ½ mv avg 2 = (3/2) kT Solve for v v rms = √(v 2 ) avg v rms = (√3kT/m)

Kinetic Energy and Temperature ½ mv 2 = KE avg = 3 / 2 kT

HEAT Calorie – Heat needed to raise 1 g of water 1 0 C Kilocalorie (Calorie) Heat needed to raise 1 kg of water 1 0 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 nRTU = Internal Energy Q = mcΔTQ = Heat c = Specific Heat Q lost = Q gained so… m 1 c 1 (T f – T 1 )+ m 2 c 2 (T f – T 1 ) =0 or… m 1 c 1 (T f – T 1 ) = m 2 c 2 (T 1 – T f )

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 = mLm = massL = latent heat

Research and Present (Separately): 1 st Law of Thermodynamics: Daniel 2 nd 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 ______