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Heat & Thermodynamics
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What is the Difference Between Heat and Temperature?
Both are related to energy but there’s a big difference
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Temperature
Measure of speed of particles (kinetic energy)
Measured by thermometers
Work by expansion of a liquid
Other types use bimetallic strip
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Digital Thermometers
Use “thermistors” - temperature dependant semiconductor resistors
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Temperature Scales
Fahrenheit T(0F) = (1.8x 0C) + 32
Celsius (centigrade)
T(0C ) = [T(0F) –32]/1.8
Kelvin (Celsius + 273)
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Examples
Zero degrees Celsius is what Kelvin?
Answer: 273o
What is the boiling point of water in degrees Kelvin?
Answer: 373o
200 degrees Celsius is what in Kelvin?
Answer: 473o
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Absolute Zero
0 degrees Kelvin = -273 Celsius
Lowest possible temperature
Molecular motion ceases
Courtesy Michigan State University
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Kinetic Theory of Heat
All matter is made of tiny atoms and molecules, constantly in motion
Faster is hotter
gas
solid
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Temperature and Kinetic Energy
In ideal gas temperature is proportional to average kinetic energy per molecule
Closely related in liquids and gases
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Temperature does not depend on the amount
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Heat does depend on the amount
Analogy: Heat is like the total height of students in this room, temperature is like their average height.
There is twice as much kinetic energy of moving molecules in two liters of water as in one liter.
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Which has more heat?
A swimming pool full of ice water?
A cup full of boiling water?
Answer: the swimming pool, because it has so much more water.
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Heat – Energy Transferred
Definition: Energy that transfers because of temperature difference
Heat flows governed by average molecular kinetic energy difference
Heat always flows from
high energy to low
Cold- Absence of Heat
* does not exist!
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Thermal Equilibrium
Objects at same temperature are at thermal equilibrium – no heat flows.
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Measuring Heat
One calorie is the amount of heat needed to raise the temperature of one gram of water by one degree Celsius.Kilocalorie raises the temperature of one kg of water by 10 C (also called Calorie or food calorie)One calorie = 4.186 joulesOne kilocalorie = 4186 joulesOne kilocalorie= 1 Food Calorie
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Density of Water
Density is mass per unit volume
D = M/V
One gram per cubic centimeter
One kilogram per liter
One thousand kg per cubic meter
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Specific Heat Capacity
Different materials change their temperature by different amounts when they absorb the same amount of heat.Some have more ways of storing energy than othersWater has very high specific heat (capacity)Metals have much less
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Q = mcT
Q = mcT expresses how heat absorption works. C is specific heat
Question: A certain rock has a specific heat of 0.25 (water is 1.0) How much heat will be required to heat 5.0 kg rock from 20 to 800C?
Q = 5.0kg x 1000g/kg x 0.25 Cal/g 0C x 60 0C
Q = 75,000 C = 7.5 x 104 Calories
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Calories
1 calorie raises the temperature of 1 gram of water by 1 Celsius degree.
1 kilocalorie (kcal or Calorie) raises temperature of 1 kg of water by 1 degree Celsius
1 British Thermal Unit (BTU) raises temperature of 1 pound of water by one degree Fahrenheit
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Application
If 10 calories of heat go into a gram of water, how much will the temperature increase?
Answer : 10 degrees CHow much heat is needed to raise the temperature of 10 grams of water by one degree C?
Answer: 10 caloriesHow much heat is needed to raise the temperature of 10 grams of water by 10 degrees C?Answer: 100 calories
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Specific Heat
How much does temperature rise when heat is put into something?It depends on the material as well as the mass and the quantity of heat:
Q = m c t c is specific heat in calories/g oCWater has the highest specific heat of any common material, 1 cal/g oCMetals generally have low specific heats, which makes them easy to cool or heat.
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Temperature ChangeExothermic Reactions, are where heat is released, this will cause the temperature of the surrounding to increase. (think a roaring fire to warm a cold room) ∆T = Tf-Ti
Endothermic Reactions, are where heat is absorbed, this will cause the temperature of the surroundings to decrease. (think ice melting in warm drink) ∆T = Ti-Tf
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Example
How much heat is required to raise the temperature of 1000g water from room temperature (20oC) to boiling (100oC)?
Q = m c t = 1000g x 1 cal/g oC x 80 oC
= 80,000 calories (or 80 kilocalories)
Fact: It would take about a tenth as much heat to raise the temperature of an equal amount of iron this much
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Other Examples
If 2000 J of energy are added to .25 kg of water at an initial temperature of 35⁰C
what will the final temperature be?
If 5000 cal are added to an unknown substance and 200 g of it change temperature by 34⁰C what is the specific heat of that substance?
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Mixtures
100 g of water at 50oC is added to 100g water at 70oC. What will be the final temperature?You guessed it: 60oC
Mix a liter of 20oC water with two liters of 30oC water. What is the final temperature of the system?
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CalorimeterEnergy device used to eliminate the loss of
energy to the surroundings.
Thermos and styrofoam cup work on same principles.
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High Specific Heat of Water
Makes it a good coolant (water also has high conductivity although this is not the same)
Large bodies of water such as oceans moderate climate – Gives coastal communities relatively mild
summers and winters
Another peculiar fact about water. It’s highest density (and smallest volume) is at 4oC.– Water at bottom of frozen lake is always 4oC
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Change of Phase
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Heat of FusionEnergy needed to melt 1 gram of a solid into its liquid form.
Hf ice= 80 cal/g
Hf= Q/m
Q= Hf x m
m= Q/Hf
This is endothermic, absorbed into the system, the same is true of the releasing, just called Heat of Crystallization.
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Heat of VaporizationEnergy needed to vaporize 1 g of some liquid into a gas.
Hv water= 540 cal/g
Hv= Q/m
Q= Hv x m
m = Q/Hv
This is endothermic as well, again being absorbed, the same is true of releasing just called Heat of Condensation.
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Phase Change Example
How many calories are required to raise the temperature of 85 grams of – 20⁰C ice to 150⁰C? (Think about all the different steps you must take to solve this problem)
∆T of icePhase change (melt the ice)∆T of waterPhase change (boil the water)∆T of steam
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Heat of Fusion Lab (Prove Hf= 80 cal/g)Cook 125 ml of water to exactly 50⁰C. Record Ti.Pour exactly 100 ml of water into sty. cup. Record Vi. (DO NOT DESTROY STY. CUPS)Add ice chips 2-3 at a time, carefully stirring with thermometer, until you reach 0⁰C. Record Tf.Carefully remove any ice chips. Record Vf.Remember Dwater 1g= 1 ml
Calculate Q (released by water)= m x ∆T x c
Calculate the mass of melted ice= Vf-Vi
Calculate the Hf of ice = Q/m
Answer this question: Why did we start at 50⁰C? Hint: Think about heat exchange and room temperature.
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Thermal Expansion
Most materials expand when heated
Only exception is water between 00C and 400C
Expansion joints in bridges, cracks in sidewalks allow for expansion
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Bimetallic Strip
How your thermostat works
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Don’t Let Your Car’s Engine Overheat
Aluminum expands more than iron
Pistons made of aluminum
Cylinder made of iron
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Mechanical Equivalent of Heat
Discovered by James Joule
Falling weight makes
paddle turn
4.186 x 103 J = 1 kcal
Interpretation:
HEAT IS ENERGY
TRANSFER
Courtesy W. Bauer http://lecture.lite.msu.edu/~mmp/kap11/cd295.htm
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Joule’s Apparatus
Link to Joule’s original article
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Example
When digested a slice of bread yields 100 kcal. How high a hill would a 60 kg student need to climb to “work off” this slice of bread?100 kcal x 4.186 x 103 J/kcal = 4.2 x 105 J
W = mgh
h = W/mg = 4.2 x 105 / (60 kg)(9.80 m/s2) =
714m = 7.1 x 102 m
If the body is only 20 percent efficient in transforming the bread, how high need they climb?
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Bullet in Block
When a 10 g bullet traveling 500 m/s is stopped inside a 1kg wood block nearly all its KE is transformed to heat. How many kcal are released?
KE = ½ mv2 = 0.5 x 0.010 kg x (500)2 = 1250 J
1250 J x 1 kcal/4186 J = 0.30 kcal
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Thermodynamics
Study of heat and its transformation into mechanical energy
Based on conservation of energy
Explains how engines like car motors work
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First Law of Thermodynamics
Generally, when you add heat to a system it changes into an equal amount of some other form of energy
Heat added = increase in internal energy + external work done by the system
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Work Done On and By
Compressing a gas by pushing down on a piston = work done on
A gas expands by pushing a piston up = work done by
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Questions
20 J of heat is added to a system that does no work. What is the change in internal energy?
Answer +20 J20 J of heat is added to a system that does 10 J of work. What is the change in internal energy?
Answer +10 J
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20 J of heat is added to a system that does 30 J of work. What is the change of internal energy?
Answer -10 J20 J of heat is added to a system that has 10 J of work done on it. What is the change of internal energy?
Answer +30 J
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Bicycle Pump
What do you think happens when you operate the pump. Where does the work you do go?It goes to heat, some through friction, some to adiabatic compression of the air inside the pumpWhat does “adiabatic” mean?Answer: No heat enters or leaves Q=0
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Adiabatic Processes
Compression or expansion of a gas so that no heat enters or leaves
Example: gas in cylinder of car or diesel engine
Why adiabatic? Because it happens too fast for much heat to enter or leave.
In adiabatic compression, temperature rises. – In diesel engine, enough to ignite gas without spark
plug
A process can also be adiabatic if it happens inside a well insulated conatiner.
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Courtesy “How Stuff Works”
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Courtesy Shell Canada
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Adiabatic Expansion
Produces cooling
Example: blow on your hand first with wide open mouth, then with puckered lips
How do you explain the results?
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The Chinook
What would you expect to happen if cold air moves down the slopes of mountains
Hint: it will be compressed by atmosphere into smaller volume
Chinook wind is warm
Common in Rocky mountains
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Second Law of Thermodynamics
Heat flows from hot to cold. By itself it will never flow from cold to hot.
Question: Would it violate the First Law of Thermodynamics (energy conservation) if heat flowed from a cold object to a warm object touching it?
Answer: No
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Second Law Applied to Engines
It is impossible to build a heat engine that changes heat completely into work.
Courtesy University of Oregon
Such an engine would be 100% efficient!
Allowed by 1st law, forbidden by 2nd law
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Heat Engine
Some heat is converted to useful workThe rest is exhausted on at a lower temperature (cause of thermal pollution)Efficiency = useful work / heat input– About 20-25% for gasoline engine– About 35-40% for diesel engine
The energy exhausted is waste, cannot be recovered
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Ideal (Carnot) Engine
Ideal (Maximum possible efficiency) = (Thot – Tcold)/Thot (Kelvin temperatures)
What is the efficiency of a steam turbine (assumed ideal) operating between 400K (1270C) and 300K (270C)?(400 – 300)/400 = ¼ or 25%What would be the efficiency if the turbine could operate at 600K?What would the exhaust temperature need to be for an engine to be 100% efficient?
1/2
0 K
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Steam Turbine
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Limits to Technology
What factors limit the efficiency of an engine?– Friction– Temperature at which parts melt– Carnot efficiency
What would be the advantages of a ceramic engine? Disadvantages?
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Courtesy University of Colorado
Can operate at 3000 degrees without cooling, is light and doesn’t need much cooling, but…
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Heat Engine Summary
Work done is difference between heat flow in at high temperature and the heat flow out at a lower temperature (conservation of energy)
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Order and Disorder
Useful energy tends to degenerate and become less usefulAlternate statement of 2nd Law: Natural systems tend toward disorderQuestion: Could all the air molecules in this room spontaneously concentrate at the top of the room (more orderly system)?
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Entropy
A measure of how much change occurs when energy spreads out according to the second law.
More generally (and less accurately) a measure of disorder
When disorder increases, entropy increases
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Mess to Neat?
Will this mess become neat all by itself?
No way!
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Will this dish reassemble all by itself?
No Way, the Second Law of Thermodynamics prohibits it
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Entropy Summary
Entropy is a quantity that measures the order or disorder of a systemThis quantity is larger for a more disordered systemThe Second Law of Thermodynamics says that entropy tends to increaseAll real engines lose heat to their surroundings
Courtesy California Science Standards in Physics
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Courtesy University of Oregon
Global Warming
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Calorimetry and Specific Heat
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Heat and Temperature Basics
Temperature does not depend on the amount
If two samples of identical material are at the same temperature, the sample with more mass has more thermal energy (internal energy)
Heat is thermal energy transferred
Internal energy is thermal energy in something
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Which Contains More Thermal Energy?
A cup of boiling water or a swimming pool frozen solid?
Answer: the swimming pool. What it loses in temperature it more than makes up in mass
This will become clearer as we learn more…
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Hot Stuff
What would happen if 1 kg iron (specific heat 0.11 calories/ g oC) at 300 oC were placed in 200g water at 20 oC?Heat lost by iron = heat gained by water
Let TW be initial temp. of water; TI that of iron; TF final temp of both
mIcI(TI-TF) = mW cW (TF – TW)
mIcI TI – mIcITF = mW cW TF - mW cW TW