Thermodynamics Test Wednesday 12/20 HEAT AND TEMPERATURE 1
Temperature Temperature: A measure of how hot (or cold) something is Specifically, a measure of the average kinetic energy of the particles in an object. If two objects of different temperatures are place in contact with one another, heat will flow from the high temp object to the low temp object. Temperature is a property that determines the direction of thermal energy transfer between two bodies in thermal contact. This flow of thermal energy will continue until the system reaches thermal equilibrium. 2
Thermometers Thermometer: an instrument that measures and indicates temperature a. b. c. Bimetallic strip Temperature Scales Kelvin International System (SI) of measurement Fahrenheit Celsius Rankine Newton Romer scale 3
Kelvin and Absolute Zero The Kelvin scale is based on absolute zero Absolute Zero: the temp at which molecular movement stops 0 K on the Kelvin scale = -273.16ºC It is the lowest temperature that can be theoretically achieved. 4
Temperatures expressed by the Fahrenheit scale can be converted to the Celsius scale equivalent using the equation below: o C o F 32 1.8 Similarly, temperatures expressed by the Celsius scale can be converted to the Fahrenheit scale equivalent using the equation below: F C1.8 32 o o o o What is heat? Heat: the transfer of energy between objects that are at different temperatures. All matter has heat. Measured in JOULES 5
Measuring Heat Flow Two Common Units Joule calorie 4.184 J = 1 cal 1Calorie = 1 kilocal = 1000 cal Heating and Cooling If an object has become hotter, it means that it has gained heat energy. If an object cools down, it means it has lost energy 6
Endothermic and Exothermic Processes Endothermic Process heat is absorbed from the surroundings Endo = Into HEAT Endothermic and Exothermic Processes Exothermic process heat is released into the surroundings Exo = Exit HEAT 7
Heating and Cooling cont Heat energy always moves from: HOT object COOLER object ex1. Cup of water at 20 o C in a room at 30 o C - gains heat energy and heats up its temperature rises ex2. Cup of water at 20 o C in a room at 10 o C loses heat energy and cools down its temperature will fall. ARE HEAT AND TEMP THE SAME THING? NO.although the two quantities are related. Example: a beaker of water at 60 o C is hotter than a bath of water at 40 o C BUT the bath contains more joules of heat energy 8
Assignment Do pg. 380-381 Problems #3,4,6,26 Thermodynamics Test Wednesday 12/20 9
Internal energy Internal energy is the total potential energy and random kinetic energy of the molecules of the substance. Microscopic scale, temp is the average kinetic energy per molecule associated with thermal motions. aka: the faster the molecule are vibrating or moving inside an object the more internal energy it possesses. Two rocks in an oven. Same heat input, different temperature rise. Internal energy = total potential + total kinetic Three (or four) Phases 10
Copper Phases - Solid Copper Phases - Liquid 11
Copper Phases Vapor (gas) 12
Measuring Heat Flow Two Common Units Joule calorie 4.184 J = 1 cal 1Calorie = 1 kilocal = 1000 cal Concept Check What causes heat to flow? Thermal energy flows from higher temp to lower temp 13
Energy Transfer The transfer of heat is normally from a high temperature object to a lower temperature object. 1) Conduction Thermal Conduction: the transfer of heat within a substance, molecule by molecule. 14
2) Convection Convection: the movement of matter due to the differences in density that are caused by temp. variations 3) Radiation Radiation: the energy that is transferred as electromagnetic waves, Doesn t need matter Most radiation comes from the sun 15
Conductor vs. Insulator Conductor: any material through which energy can be transferred as heat Insulator: poor conductors Thermal Capacity Of a particular body is the energy required to raise the temperature of that body by 1 C. ChangeInThermalEnergy ThermalCapacity ChangeInTemperature C Q T 16
A 2 kg cylinder of copper is heated from room temperature (20 C) to 500ºC. 374kJ of thermal energy were transferred to the copper during the heating process. Calculate the thermal capacity of this piece of copper. 374000J o C 780 J / C o 500 20 C A 25kg cylinder of copper is heated from room temperature. The same 374kJ of thermal energy were used during the heating process but this time the copper s temperature rose from room temperature to only 58.4ºC. Calculate the heat capacity of this piece of copper. 374000J o C 9740 J / C o 58.4 20 C 17
Assignment Thermodynamics Assignment #2 on the website Thermodynamics Test Wednesday 12/20 18
Specific Heat Adding energy to a material causes the temperature to go up. Taking energy away from a substance causes the temp. to go down! Have you ever noticed that on a hot summer day the pool is cooler than the hot cement? OR maybe that the ocean is cooler than the hot sand? Why? The sun has been beating down on both of them for the same amount of time... It takes more thermal energy to raise the temperature of water that it does the cement! 19
Water absorbs a lot of heat energy before its temperature changes while sand needs little heat energy before its temperature increases. Specific Heat Specific Heat The amount of energy required to raise the temperature of a material (substance). It takes different amts of energy to make the same temp change in different substances. We call the amt required: Specific Heat! 20
The specific heat capacity of a particular substance is equal to the energy required to raise the temperature of a unit mass of the substance by 1ºC Specific Heat of water The Cp is high because H 2 O mols. form strong bonds w/each other. It takes a lot of energy to break the bonds so that the the molecules can then start to move around faster (HEAT UP). 21
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Calculating Specific Heat The Greek letter Δ means change in Solving for specific heat There are two methods common for measuring the specific heat capacity. Electrical If an electrical immersion heater is place into a solid or a liquid, then the energy from the heater will be transmitted by conduction into the substance and the substance will get hotter. Mixtures If a hot object is place next to a cooler one (or placed into it if the cooler one is liquid), then the cooler substance will gain energy and become hotter and the hotter object will lose energy and become cooler until both objects come to the same temperature called thermal equilibrium. 23
A 2kg cylinder of copper is heated from room temperature(20ºc) to 500ºC. 374kJ of thermal energy were transferred to the copper during the heating process. Calculate the specific heat capacity of this piece of copper. o 374000 J c(2 kg)(480 C) 374000 960c o c 390 J /( kg C) A 25kg cylinder of copper is heated from room temerature. The same 374kJ of thermal energy were used during the heating process but this time the copper s temperature rose from room temperature to only 58.4ºC. Calculate the specific heat capacity of this piece of copper. o 374000 J c(25 kg)(38.4 C) 374000 960c o c 390 J /( kg C) 24
Substance: Wood Mercury Alcohol Water (Ice) Water (Liquid) Water (Steam) Specific Heat Capacity 1700 J/(kg C) 140 J/(kg C) 2400 J/(kg C) 2100 J/(kg C) 4200 J/(kg C) 2010 J/(kg C) A 240V electric heating element is used to heat water. The temperature of the water rose from 20ºC to 50ºC in 4minutes 20 seconds. During the heating process, the current flowing in the heater was measured to be 3.54A. Calculate the mass of the water. Power VoltageCurrent P (240 V )(3.54 A) 850W 850 J / s 4 min 20sec 260sec Q (850 J / s)(260 s) 221000J o o 221000 J (4200 J / kg C) m(30 C) m 1.75kg 25
The 850W heater was then placed into a hole in a piece of copper of mass 1.75kg. (A) Calculate the temperature rise in the copper if the heater was left on for 4min 20sec. (B) Calculate the final temperature of the copper if the heater was left on for 10min and the copper was originally at a temperature of 65ºC. a) P 850W 850 J / s 4 min 20sec 260sec Q (850 J / s)(260 s) 221000J o 221000 J (385 J / kg C)(1.75 kg)( T ) o T 328 C b) P 850W 850 J / s 10 min 600sec Q (850 J / s)(600 s) 510000J o 510000 J (385 J / kg C)(1.75 kg)( T 65) o T 822 C A block of substance X has a mass of 100g and is heated to 260ºC. The block is then placed into a beaker containing 500g of water at 20ºC. After some time both substances reach their equilibrium temperature of 30ºC. Calculate the specific heat capacity of substance X. Energy gained by the water = Energy lost by X m c T m c T w w W x x x o o o (.5 kg)(4200 J / kg C)(10 C) (.1 kg) c(230 C) 21000 23c o c 913 J / kg C 26
A 0.5kg block of copper (specific heat capacity 385J/kgºC) at an initial temperature of 420ºC was placed into 1.3kg of water at 40ºC. What will be the final temperature of the mixture when thermal equilibrium is reached? m c T m c T c c c w w w o o o o (.5 kg)(385 J / kg C)(420 C T ) (1.3 kg)(4200 J / kg C)( T 40 C) 80850 192.5T 5460T 218400 5652.5T 299250 o T 52.9 C Assignment Thermodynamics Assignment #3 on the website 27
Thermodynamics Test Wednesday 12/20 Now to a mole! The mole is a counting unit The mole (mol) is the SI unit used to measure the amount of a substance. It is based on the number of atoms in 12g of carbon We can convert number of particles to moles and moles to particles. 28
What is a mole? One mole of anything consist of 6.02x10 23 units of that substance. How many eggs are in a mole of eggs? How many paper clips are in a mole of paper clips? How many shoes are in a mole of shoes? Answer: 6.02x10 23 eggs, paper clips, shoes Avogadro s Number as Conversion Factor 23 6.02x10 particles 1mole or 1mole 23 6.02x10 particles Note that a particle could be an atom, a molecule or anything!! 29
Just How Big is a Mole? Enough soft drink cans to cover the surface of the earth to a depth of over 200 miles. If you had Avogadro's number of unpopped popcorn kernels, and spread them across the United States of America, the country would be covered in popcorn to a depth of over 9 miles. If we were able to count atoms at the rate of 10 million per second, it would take about 2 billion years to count the atoms in one mole. The Mole This photograph shows one mole of salt(nacl), water(h 2 O), and nitrogen gas(n 2 ). 30
We also know 1 mole of an element s atoms is equal to that element s average atomic mass (expressed in g) Example We have an unknown # of H atoms. We want to know many H atoms are present? We weigh the sample, results =.5g 31
Example 1 mol (.5 g H) 0.496 mol 1.008 g H (.496 mol of H) 23 6.02x10 H atoms 1 mol 23 2.99x10 H atoms Example Convert 38g of P into # of atoms 30.974 g P 1 mol 23 1 mol 6.02x10 P atoms 23 (38 g P) 7.4x10 atoms of P Convert 1.25 mol of Ag into # of atoms 23 6.02x10 Ag atoms 23 1.25 mol of Ag 7.5x10 atoms of Ag 1 mol 32
How many moles are in 15 grams of lithium? How many atoms? 1 mol (15 g Li) 2.16 mol of Li 6.941 g Li 23 6.02x10 Li atoms 24 2.16 mol of Li 1.3x10 atoms of Li 1 mol How many grams are in 2.4 moles of sulfur? How many atoms? 32.066 g of S (2.4 mol of S) 76.96 g of S 1 mol of S 23 6.02x10 S atoms 24 2.4 mol of S 1.4x10 atoms of S 1 mol 33
Molar Mass Chemical compounds have multiple parts like the sucker. Ex. Methane (natural gas) CH 4 1 CH 4 molecule With 5 parts (1 C atom and 4 H atoms) Molar Mass In 1 mol of a molecule there are corresponding moles of its parts. Ex. In 1 mol of CH 4 there are 1 mol of C and 4 mol of H 34
Molar Mass How do we figure out the mass of 1 mol of methane? We break it down in to its parts and add them up. This is called the molar mass. Molar Mass- is the mass of a molecule Total mass of all the parts of a molecule Example: SO 2 What is the molar mass of SO 2? Mass of 1 mol of S (1)(32.07 g) 32.07g Mass of 2 mol of O (2)(16.00 g) 32.00g Mass of 1 mol of SO 32.07g32.00g The molar mass of SO 64.07g 2 2 35
Example: CaCO 3 What is the molar mass of CaCO 3? Mass of 1 mol of Ca (1)(40.08 g) 40.08g Mass of 1 mol of C (1)(12.01 g) 12.01g Mass of 3 mol of O (3)(16.00 g) 48.00g Mass of 1 mol of SO 40.08g 12.01g 48.00g The molar mass of SO 100.09g 2 2 What is the molar mass of water, H 2 O? (2)(1.01 g) (1)(16.00 g) 16.01g What is the molar mass of ammonia, NH 3? (1)(14.01 g) (3)(1.01 g) 17.04 g What is the molar mass of propane, C 3 H 8? (3)(12.01 g) (8)(1.01 g) 44.11g 36
Assignment Thermodynamics Assignment #4 on the website Thermodynamics Test Wednesday 12/20 37
Micro Properties of different phases Solids Strong bonds between atoms Lowest internal energy Atoms in fixed positions vibrating/oscillating Liquids Weaker forces. Some bonds are broken More internal energy Atoms can move about and change places Gases Virtually no forces/bonds High internal energy Atoms completely free to move at high speed Macro Properties of different phases Solids Maintain shape Lowest temp Low compression/expansion Liquids Takes the shape of its container Moderate temp Low compression/expansion Gases Fills the container Highest temp High compression/expansion 38
Plasmas atoms are at extremely high temperatures and are ionized. Usually found in stars. Evaporation vs Boiling in fluids Molecules movement is completely random Some high, some low. As collisions occur, energy transfers from one molecule to another. Eventually the kinetic energy > intermolecular binding energy The individual molecules can break free from the surface. 39
Phase Change Solid substance is heated Gains thermal energy(kinetic) and molecular thermal motion Average molecular thermal energy becomes the same as the intermolecular binding energies, a phase change occurs. Crystal lattice can be broken and the solid melts. This is the MELTING POINT! Phase Change Detailed Once the temp. has reached the melting point, the thermal energy is used to break bonds. Substance gains potential energy, not kinetic. Meaning no rise in temperature until all the substance has melted. This can be applied to: liquids turning into gas Gas turning into liquids Liquids turning into solids 40
Lets look at what happens at each jump/step. Latent Heat Latent heat is the energy absorbed during a phase change. It does not increase the kinetic energy of the substance Associated with no temperature rise. Increases the potential energy Latent heat of fusion Solid to liquid Latent heat of vaporization Liquid to gas 41
Latent Heat Formula SpecificLatentHeat changethermalenergy mass L Q m Unit is J/kg or J kg -1 Data book: Q = ml Example Calculate the total energy that must be transferred to a 0.5kg block of ice at -12ºC if it is to be completely converted into 0.5kg of steam at 108ºC. Solution: This is essentially 5 separate calculations. The 5 steps are the steps from: 1. A B 2. B C 3. C D 4. D E 5. E F 42
Step one The energy required to raise the temperature of the ice from 12ºC to 0ºC Q 1 1 1 1 o 1 o Q 1 (0.5 kg)(2100 J kg C )(0 ( 12) C) Q 12600J 1 mc T Step two The energy required to melt the ice (at 0ºC) Q 2 5 1 Q 2 (0.5 kg)(3.3x10 J kg ) Q 165000J 2 ml fusion 43
Step three The energy required to raise the temperature of the water from 0ºC to 100ºC Q 3 3 3 1 o 1 o Q 3 (0.5 kg)(4200 J kg C )(100 0 C) Q 210000J 3 mc T Step four The energy required for the water to turn to steam (at 100ºC) Q 4 6 1 Q 4 (0.5 kg)(2.27x10 J kg ) Q 1135000J 4 ml vaporization 44
Step five The energy required to raise the temperature of the water from 100ºC to 108ºC Q 5 5 5 1 o 1 o Q 5 (0.5 kg)(2100 J kg C )(108 100 C) Q 8400J 5 mc T Final Q Q Q Q Q Q 1 2 3 4 5 Final Q 12600 165000 210000 1135000 8400 Final Q=1531000 J or 1531 kj Specific Latent Heat We can find specific latent heats of fusion and vaporization of a substance by using the mixture and electrical methods as well. Mixture Method Lump of ice is dropped into water Thermal energy transferred to ice. Temp of ice increases until it starts to melt @ 0ºC Energy then goes into breaking bonds. Once all ice has melted, the temp of liquid will rise. A calorimeter with known specific heat and mass is usually used because the container s temp will also drop the the same equilibrium temp. Calculations should be adjusted to incorporate the cooling of the container. 45
Example 11 50g of ice 0ºC is dropped into a beaker containing 200g of water initially at 30ºC. If the final temperature of the mixture is 10.2ºC, calculate the specific latent heat of fusion of ice. Solution: Energy from the water = Energy to the ice The energy to the ice, is in two stages though. The first stage is in the melting the ice at 0ºC, the second is in raising the temp of the ice from 0ºC to 10.2ºC. Answer: without calorimeter = 289800Jkg -1, with calorimeter = 312966Jkg -1. Specific Latent Heat We can find specific latent heats of fusion and vaporization of a substance by using the mixture and electrical methods as well. Electrical Method similar idea Electric heating element is put in water Temp of water will rise as thermal energy is absorbed Once temp is 100ºC energy goes to breaking bonds Mass of water will go down as the stem leaves the container Specific latent heat of vaporization for water can then be calculated by examining the loss of mass and the energy input to the water. 46
Example 3kg of water at 20ºC were put into an electric kettle with a power rating of 2kW and heated until it boiled. Once boiling the kettle continued to transfer thermal energy to the water for a further 6 min. The mass of the water after this time was seen to drop to 2. 68kg. Calculate the specific latent heat of vaporization for water. Solution Energy from the kettle to the water = power x time Q = ml Q (2000 W )(360sec) 720000J Q ml 720000 (3kg 2.68 kg) L L 2250000 J kg 1 Example 1.5 kg of water at 25ºC were put into an electric kettle with a power rating of 2.5kW and heated. Calculate the time taken to boil the water off completely. (i.e. all the water turned into steam). Solution: Energy needed = Energy to raise temp to 100ºC + Energy to convert water to steam The kettle supplies 2500J of energy every second T = Q / P Q (1.5 kg)(4200)(100 25) (1.5 kg)(2264000) Q 3.86x10 6 J 6 3.86x10 J Time 1544sec 25.73min 2500 J / s 47
Pressure Gas molecule movement is random. (speed/direction) Collisions occur all the time. (molecules/container) Pressure is the result of these collisions. On a microscopic scale, pressure is the result of the force imparted on the area of a container wall due to the change in momentum of the colliding molecules. Pressure = Force / Surface Area Pressure = F/A Equations PV nrt R 8.31 J K mol 1 1 2 2 1 1 2 2-1 -1 (Pressure)(Volume) (number of moles)(r)(temp) PV n T PV n T 48
Summarized If volume is ½ed, then molecules are closer together and therefore have twice as many collisions. Also, twice the collisions means double the pressure. If volume is constant, and temp is increased, then pressure will increase. Example How many moles of gas are there in a gas of temp 300K, volume.02m 3 and pressure of 2 x10 5 Pa. PV nrt (200000)(.02) n(8.31)(300) 4000 2493n n 1.6mol 49
Example A container of hydrogen of volume 0.1 m 3 and temp of 25ºC contains 3.2x10 23 molecules. What is the pressure in the container? 3.2x10 n 6.02x10 PV nrt 23 23 4 1.3x10 Pa 0.53 mol P(.1) (.53)(8.31)(298).1P 1312 P Example A gas of volume 2L, pressure 3atm and temp 300K expands to a volume of 3 L and a pressure of 4 atm. What is the new temperature of the gas? PV n T PV n T 1 1 2 2 1 1 2 2 (3)(2) (4)(3) n(300) nt 6 12 300 T 6T 3600 T 600K 2 50
Assignment Thermodynamics Assignment #5 on the website 51