Thermodynamics. Ch 12 - 15. Thermal Energy. Internal energy of a system (kinetic energy of the particles that make up the thing) Types of Substances Gas: particles move freely Liquids: some particles move freely and some are weakly bonded

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Thermodynamics

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Thermal Energy • Internal energy of a system (kinetic energy of the particles that make up the thing) • Types of Substances • Gas: particles move freely • Liquids: some particles move freely and some are weakly bonded • Solids: particles move some (as if attached to springs), much stronger bonds (chemical bonds)

Thermal Definitions • Thermal Contact two systems are placed so that they can exchange thermal Energy • Heat thermal energy TRANSFERRED from one system to another. • TemperatureAVERAGE KINETIC ENERGY of the particles in a system. • Thermal equilibrium A static state. Objects in thermal contact reach the same average internal energy state and no longer exchange thermal energy.

Temperature • Measured with thermometer • Scales: Celsius, Kelvin, Fahrenheit

Celsius • Originally set up to monitor temperatures of earth’s surface • 0 degrees = freezing point of water • 100 degrees = boiling point of water at 1 atm

Kelvin • Has a true zero • Absolute zero: lowest possible energy state for matter • Zero Kelvin = -273.15 degrees Celsius • Freezing point of water = 273.15 K • You don’t use the word “degrees” • “Hey it’s three hundred and one Kelvins outside!”

What happens to heated stuff • Particles gain KE • Temperature increases • Particles move faster and further • Particles take up more room • Object expands in all directions • Architects and engineers must account for this in their designs: • Expansion joints on bridges, sidewalks, etc

Change in size depends on: • Amount of temperature change • Identity of substance Coefficient of linear expansion

Ex 2: A brass rod 5m long and 0.01 m in diameter increases in length by 0.05m when its temperature is increased by 500oC. A similar brass rod of length 10m has a diameter of .02m. By how much will this rod’s diameter increase if its temp. is increased by 1000oC?

Thermostats • Made of bimetallic strips - two metals bonded together • Metals expand different amounts • So, one metal expands more than the other • Causes strip of metal to curve when the temperature changes • Used to switch electrical circuits on and off • Thus, controlling an air conditioner/ heater

How it works • You move lever to turn “up” the heat • Coil and mercury switch tip to left • Current flows through mercury in switch • Heater kicks in • As room heats up, coil gradually unwinds • Mercury switch tips right – breaking circuit • Heater turns off

Heat Flow • Must be a temperature difference • Greater the difference, faster the heat flow • Flows from high to lower temperatures • ΔT= Temperature Difference

Flow of Heat Through a Slab Rate of heat transfer is proportional to amount of heat that travels through the object per time

Thermal Conductivity • Amount of heat that makes it through the slab depends on thickness, surface area and thermal properties (thermal conductivity) • Ability of a substance to transfer heat • Symbol is “k” • Large k = good conductors • Flow Rate Equation: Area Thickness of material Heat Flow Rate Thermal conductivity (J/s, J/min, Cal/h, etc)

Since and substituting in for H, we get: This would give us the amount of heat flow that would occur in a given time

Ex 3: A brick oven is 15.0 cm thick. The inside temperature is 350.0 C. The outside temperature is 25.0 C. How much heat is lost from one side of the oven in one hour? The side measures 85.0 cm x 60.0 cm. Thermal conductivity of brick is 0.71 J/smC.

Mechanical Equivalent of heat • 1800’s Joule discovered that HEAT and MECHANICAL ENERGY are equivalent • Amount of work done by the weight was equal to the thermal energy that increased the water’s temperature

Units for measuring heat • calorie: amount of heat it takes to raise the temperature of one cubic centimeter of water by one degree Celsius • 1 cal = 4.186J • 1000 cal = 1 kcal = 1 Cal (“food” Calories)

Ex 5: A serving of fried frog legs provides 876 Cal per serving. If you eat two servings, How many joules of mechanical work must you do to “burn off” the frog leg calories? If you climbed a staircase to work off the frog legs, how high would you have to climb? You have a mass of 58kg. (a) That’s a lot of joules! (b) That’s a lot of stair climbin’.

Specific Heat Heat to raise the temperature of one gram of a substance by one degree Celsius. The heat required to raise a substance’s temperature is given by this equation: Q is the heat absorbed/released m is the mass of the substance c is the specific heat T is the temperature difference

Ex 4: An aluminum rod (ρ=2.7 X 103kg/m3) has a radius of .01m and an initial length of 2m at a temp. of 20oC. Heat is added to raise its temp. to 90oC. Its coefficient of linear expansion is α=25X10-6/oC, the specific heat is cal=900J/kgoC, and a thermal conductivity of k=200J/smoC.a) What is the mass of the aluminum rod?b) What is the amount of heat added to the rod?c) What is the new length of the rod?d) If we were to use this rod to transfer heat between two objects one side being at 20oC and the other side at 90oC, what would the rate of heat transfer be?

Law of Heat Exchange (The Zeroth Law of Thermodynamics) The heat lost by the hot system is equal to the heat gained by the cold system QLost = QGained

Ex 7: A 235 g gold ball at a temperature of 125C is dropped into an insulated flask of water. The water was initially at a temperature of 22C. If the equilibrium temperature is 25C, what is the mass of the water?

Ex 8: A 158.0 g brass ball at a temperature of 265 C is dropped into a container containing 550.0 g of water. If the final temperature of the ball is 35.5 C, what was the initial temperature of the water?

Heat required for a phase change Q is heat m is mass L is the latent heat for the phase change The latent heat of vaporization has this symbol: Lv The latent heat of fusion has this symbol: Lf

An aluminum rod (density = 2.7X103kg/m3) has a radius of .01m and an initial length of 2m at a temp of 20 oC. Heat is added to raise its temp to 90oC. Its coefficient of linear expansion is 25X10-6/oC, the spec. heat is 900J/kgoC, and a thermal conductivity of 200J/smoC.A) What the mass of the aluminum rod?B) What is the amount of heat added to the rod?

Three ways of heat transfer • Conduction: transfer by direct contact • Sit on a hot car seat • Touch a hot pan • Transfer occurs until equilibrium is reached • Radiation: transfer by electromagnetic waves • A lot of the energy from the sun • Glowing red heat elements of space heaters • Heat from a fireplace/camp fire • Convection: transfer by fluid flow • Heat in homes via forced air furnaces • Ovens: heated air circulates around and around

Heat Transfer by Conduction • Conductor: material in which heat flows easily • Metals b/c of metallic bonds (have “community electrons” or free electrons) • Insulator: does not allow heat to flow • Gases b/c not many particles • Vacuum is even better • Materials with lots of air pockets • Thermos bottles have • Vacuum – excellent insulator • Glass – good insulator • Mirror - prevents radiation

Kinetic Theory The study of matter, particularly gases, as very small particles in constant motion.

Kinetic Theory Main assumptions: • Perfectly Elastic Collisions • Random Movement • All particles are identical • No forces of attraction b/t gas particles • Enormous # particles and separation b/t

More about gas particles… • Molecules move freely and rapidly • Confined gas exerts a force on walls of container • SI Unit for pressure = N/m2, the pascal (Pa) • One mole of atoms = NA= 6.022 X 1023 atoms • That’s Avogadro’s number • 1mol of an atom = atomic molecular mass in GRAMS • 1 mol of C = 12g • 1 mol of CO2 = 12g + 2(16g) =44g

Thermodynamic State The thermodynamic state of a gas is defined by four coordinates: • Absolute pressure, P • Absolute temperature, T • Volume, V • Mass mor quantity of matter n

P1, V1 T1 m1 P2, V2 T2 m2 Gas Laws Between States Boyle’s Law, Charles’ Law, andGay-Lusac’s Lawcan be combined into a single formula for an ideal gas that changes fromState 1to anotherState 2. State 1 State 2 Any Factor that remains constant divides out

Example 10: An auto tire has a gauge pressure of 28 psi in the morning at 200C. After driving for hours the temperature of air inside the tire is 300C. What will the gauge read? (Assume 1 atm = 14.7 psi.) T1 =20 + 273 = 293 K T2 =30 + 273 = 303 K Pabs = Pgauge + 1 atm;P1 = 28 + 14.7 = 42.7 psi Same air in tires: m1 = m2 Same volume of air: V1 = V2

Given: T1 = 293 K; T2 = 303 K; P1 = 42.7 psi Example 10: What will the gauge read? P2 = 44.2 psi Gauge pressure is 14.7 psi less than this value: P2 = 44.2 psi - 14.7 psi ; P2 = 29.5 psi

Volume of one mole of a gas: V = 22.4 L or 22.4 x 10-3 m3 Ideal Gas Law Substituting moles nfor mass m, we know that: In other words, the ratio PV/nT is a constant, and if we can find its value, we can work with a single state. Since a mole of any gas contains the same number of molecules, it will have the same volume for any gas.

The Universal Gas Constant R The universal gas constant Ris defined as follows: Evaluate for one mole of gas at 1 atm, 273 K, 22.4 L. R = 8.314 J/mol·K

Ideal gas law can also be written: P = Pressure (Pa=N/m2) V = Volume (m3) Remember: 1L = 10-3m3 N = number of molecules kB = Boltzmann’s constant 1.38 X 10-23 J/K T = Temp (Kelvin)

For fixed volume of a gas, P↑ T↑ P ↑ when gas molecules strike sides of container with more force More force occurs when molecules move faster Force is RATE OF CHANGE IN MOMENTUM