1. This Week Heat and Temperature Water and Ice
Our world would be different if water didn’t expand
Engines
We can’t use all the energy!
Why is a diesel engine more efficient?
Geysers: You have to be faithful
11/12/2018
Physics 214 Summer 2017

2. Heat
Heat is a form of energy and any object has internal energy in the form of kinetic energy of the atoms or molecules and in potential energy connected with the molecular structure and the electromagnetic forces among the constituents.
If we add energy to an object the internal energy increases.
Energy can be added in many ways. For example we can do work such as
the frictional forces on a moving object.
electromagnetic radiation from the sun.
a source of heat like a hair dryer.
11/12/2018
Physics 214 Summer 2017

3. First Law of Thermodynamics
The increase in the internal energy of a system is equal to the amount of heat added to the system minus the amount of work done by the system.
U = internal energy
Q = heat that is added or removed
Wsystem = is the work done by the system
Compression the force pushing on the piston does positive work and puts energy into the gas.
The work done by the gas is negative
Expansion The gas pushing on the piston does positive work and energy is removed from the gas
The work done by the external F is negative
ENERGY CONSERVATION
ΔU = Q – Wsystem or ΔU = Q + Wexternal
Compression Q W U
Expansion
11/12/2018
Physics 214 Summer 2017

4. Temperature
Heat flows from a hot body to a cold body until they reach thermal equilibrium.
Temperature is the quantity that measures whether one body is hotter than another and at thermal equilibrium both bodies have the same temperature.
The simplest picture
is a gas of free molecules where the energy
is kinetic. A higher temperaturemeans higher
velocities and more stored energy.
Increase U and T increases
11/12/2018
Physics 214 Summer 2017

5. Measuring temperature
Physical properties of an object change with temperature. For example mercury expands as the temperature increases and we can use that expansion to measure T.
There are three temperature scales,
Celsius, Fahrenheit and Kelvin
Mixture of ice and water C F K
Boiling point of water C F K
Tc = 5/9(Tf – 32) Tf = 9/5Tc TK = Tc + 273
Note that the temperature at which water boils depends on the value of the atmospheric pressure so that at higher altitudes water boils at a lower temperature
11/12/2018
Physics 214 Summer 2017

6. Absolute zero An ideal gas obeys the law PV = constant x T
if we keep V constant the pressure is proportional to T.
If we measure P versus T at constant volume we find a temperature where the pressure is zero. This is absolute zero where the stored internal energy has it’s lowest possible value.
This is Zero degrees Kelvin
11/12/2018
Physics 214 Summer 2017

7. Heat capacity
For a given object at a specific temperature the total internal energy depends on how big the object is. If we add a fixed amount of energy the temperature will rise but the rise will be smaller the larger the object is. So we define a quantity called specific heat
c = is the quantity of heat required to raise unit mass of a substance by one degree.
Q = mcΔT
New unit
1 calorie = heat required to raise 1 gram of water 10C calorie = joules
Note to raise 1kg of water 10C requires 1000cal
Note that internal energy can change without a temperature change. This is due to internal rearrangement of the molecules
Ice Water
11/12/2018
Physics 214 Summer 2017

8. Water and Ice
Water has an unusual behavior as the temperature is changed. As we lower the temperature from room temperature it shrinks but it 40C it starts to expand and that is why ice floats.
Remember density ρ = mass/volume so below 40C the volume increases and the density decreases.
Above 40C the molecules are tightly packed. Below 40C the molecules form a crystalline structure that has holes.
11/12/2018
Physics 214 Summer 2017

9. Change of state
We are used to solids, liquids and gases and that most substances can be in any of the three states depending on temperature and pressure. Solids have more orderly structure and the atoms/molecules are tightly joined. In a liquid the atoms/molecules are loosely joined. In a gas the atoms/molecules are “free”. When we tear apart something that is joined energy is required and this is true as we go from solid to liquid and liquid to gas. Taking water as an example
80 calories/gram are required to melt ice at 0oC to water at 0oC and 540 calories/gram to convert water to gas at 100oC. When water freezes 80cal/gm has to be removed and when water condenses 540 cals/gm is released.
80 cals/gm is the latent heat of fusion
540 cals/gm is the latent heat of vaporization
11/12/2018
Physics 214 Summer 2017

10. Gases
Work done by gas = -Fd = -PAd
ΔV = Ad W = -PΔV
External work done = W = P ΔV
A quantity of gas can be described by three variables. Pressure, volume and temperature
U = internal energy (kinetic energy of the molecules)
U determines the temperature
Q = heat energy that is put in or taken out
Wgas = work done by the gas when it expands
or is compressed
Wgas is + if it expands – if it is compressed
11/12/2018
Physics 214 Summer 2017

11. Physical Laws for a gas Energy conservation
ΔU = Q + Wexternal (or ΔU = Q - Wgas )
Ideal gas law PV = NkT (T in degrees Kelvin)
Adiabatic no heat in or out Q = 0
Compression external work is (ΔU, T increase)
Expansion external work is – (ΔU, T decrease)
Isothermal T does not change ΔU = 0 Q = W = PΔV
put in heat gas expands take out heat gas must be compressed
Isobaric pressure is kept constant
Put in heat T increases gas expands (hot air balloon
11/12/2018
Physics 214 Summer 2017

12. 3E-03 Fire Syringe
Compression and rise in air temperature
What will happen to the combustible material when the plunger is rapidly pushed down ?
Can you guess the every-day application of this phenomenon ?
This system is analogous to the combustion cycle within a diesel engine or any fuel injected engine.
RAPID COMPRESSION IS ADIABATIC GIVING RAPID RISE OF AIR TEMPERATURE IN THE CHAMBER WHICH EXCEEDS THE IGNITION TEMPERATURE OF THE FLAMMABLE MATERIAL.
11/12/2018
Physics 214 Summer 2017

13. Solids and liquids Temperature depends on the internal energy
Put in heat T rises except at a change of state
We define the specific heat c as the amount of heat
required to raise unit mass of a substance by one degree.
Q = mcΔT
The usual unit is calories/gram/0C cal = joules
The specific heat of water is 1cal/gm/0C
Change of state
ice water steam
Requires 80 cal/gm to melt ice at 0C to water at 0C
Requires 540cal/gm to make steam at 1000C
To condense steam or freeze water requires the removal of 540 cal/gm or 80cal/gm.
Q = mciceΔT Q = m Q = mcwaterΔT Q = m540
-T Steam Q
11/12/2018
Physics 214 Summer 2017

14. Heat engines
The use of energy and the conversion of energy is essential not only in our practical everyday life but is a requirement for life to exist. The sun puts energy into the earth and we use such energy sources as gasoline, coal and nuclear power.
The conversion of one form of energy into another form of energy is governed by the physical laws. The generic term used is a heat engine for any system that takes an energy source and uses it to produce work.
A car engine is a practical example.
Of course there is a practical aspect that an energy source can become depleted, like oil but we will find that there is a fundamental law that prevents the utilization of all the available energy.
11/12/2018
Physics 214 Summer 2017

15. 2nd Law of Thermodynamics
Heat engine uses energy QH and produces work W and releases Qc
Efficiency = ε = W/QH
W = QH – Qc (c = environment)
2nd law
No engine working in a continuous cycle can take heat at a single temperature and convert that heat completely to work.
11/12/2018
Physics 214 Summer 2017

16. Carnot Cycle
We can design a “perfect engine” without friction. The Carnot cycle is is an ideal engine and an analysis reveals that
ε = (TH –Tc)/TH (T in oK)
For example in a gasoline engine TH is the temperature of combustion and Tc is outside temperature. If we take TH as 1500o and Tc as 300o then ε = 80%. In practice the efficiency is maybe 35%.
11/12/2018
Physics 214 Summer 2017

17. Car engines
In an engine with spark plugs a gasoline/air mixture is compressed and the temperature rises and then the spark ignites the mixture before it reaches the combustion temperature. For increased efficiency one would like to reach as high a temperature as possible so fuel injection solves this problem by compressing air and injecting the fuel after the combustion temperature is reached.
Turbo charged engines force more air into the chamber when the piston reaches it’s lowest point using power from the engine. Super chargers do the same thing but with an extra electrical motor. This causes the engine to run hotter.
Diesel engines use a lower grade of petroleum and also runs at a much higher temperature
11/12/2018
Physics 214 Summer 2017

18. Review Chapters 10 and 11 W = PΔV for the piston shown
Wexternal = + Wsystem = -
ΔU = Q – Wsystem or ΔU = Q + Wexternal
Temperature scales Celsius, Fahrenheit Kelvin
Mixture of ice and water C F K
Boiling point of water C F K
Tc = 5/9(Tf – 32) Tf = 9/5Tc TK = Tc + 273
c = is the quantity of heat required to raise unit mass of a substance by one degree.
Q = mcΔT
1 calorie = heat required to raise 1 gram of water 10C = joules
Change of state (internal energy changes temperature is constant)
80 cals/gm is the latent heat of fusion
540 cals/gm is the latent heat of vaporization
Work done on gas = Fd = PAd
ΔV = Ad W = PΔV
Work done by gas is -W
11/12/2018
Physics 214 Summer 2017

19. Gases Work done by gas = -Fd = -PAd ΔV = Ad W = -PΔV
External work done = W =P ΔV
Energy conservation
ΔU = Q – Wgas
Ideal gas law PV = NkT (T in degrees Kelvin)
Adiabatic no heat in or out Q = 0
Compression work is (ΔU, T increase)
Expansion work is – (ΔU, T decrease)
Isothermal T does not change ΔU = 0 Q = W = PΔV
put in heat gas expands take out heat gas must be compressed
Isobaric pressure is kept constant
Put in heat T increases gas expands (hot air balloon)
11/12/2018
Physics 214 Summer 2017

20. Heat engines TH ε = (TH –Tc)/TH (T in oK) Tc Efficiency = ε = W/QH
Change in internal energy in one cycle is zero
W = QH – Qc (c = environment)
2nd law
No engine working in a continuous cycle can take heat at a single temperature and convert that heat completely to work.
Perfect engine (no friction )
ε = (TH –Tc)/TH (T in oK) Tc
11/12/2018
Physics 214 Summer 2017

21. Our World
11/12/2018
Physics 214 Summer 2017

22. Geysers (Old Faithful)
Geysers produce a jet of water very often at equal time intervals. Old Faithful in Yellowstone erupts every 90 minutes or so. What is required is a source of heat, a source of water and a constricted vertical channel that the water flows into.
As the column of water increases in height the pressure increases at the bottom of the water column where the heat is. The increase in pressure raises the boiling point. This continues until the water at the bottom starts to boil.
This causes an expansion of the column which reduces the pressure and
immediately takes the temperature of all the water below the boiling point and there is an explosive boiling resulting in the eruption.
P = ρgh
Heat
11/12/2018
Physics 214 Summer 2017

23. Worked Questions and Problems
11/12/2018
Physics 214 Summer 2017

24. Questions Chapter 10
Q1 Is an object that has a temperature of 0°C hotter than, colder than, or at the same temperature as one that has a temperature of 0°F?
Water freezes at 0o C and 32o F so 0o F is colder
Q2 Which spans a greater range in temperature, a change in temperature of 10 Fahrenheit degrees or a change of 10 Celsius degrees?
There is 100o C between water freezing and boiling and 180o F so 1oC = 1.8oF so a change of 10oC is larger
11/12/2018
Physics 214 Summer 2017

25. Q5 Is it possible for a temperature to be lower than 0°C?
Q4 We sometimes attempt to determine whether another person has a fever by placing a hand on their forehead. Is this a reliable procedure? What assumptions do we make in this process?
Body temperatures internally are very similar for all people so in principle we can tell if a temperature is elevated just like any other hot object. The assumption is that your hand is at body temperature.
Q5 Is it possible for a temperature to be lower than 0°C?
Yes. Absolute zero is – 2730 which one can think of as the place where the molecules of an ideal gas have zero energy
Q6 Is it possible for a temperature to be lower than 0 K on the Kelvin temperature scale?
Yes. Absolute zero is – 2730K
11/12/2018
Physics 214 Summer 2017

26. Q8 Two objects at different temperatures are placed in contact with one another but are insulated from the surroundings. Will the temperature of either object change?
They will exchange heat until they both reach the same temperature
Q10 Two objects of the same mass, but made of different materials, are initially at the same temperature. Equal amounts of heat are added to each object. Will the final temperature of the two objects necessarily be the same?
No. The specific heat, which is the heat energy required to raise the temperature one degree, is different for each material
Q13 What happens if we add heat to water that is at the temperature of 100°C? Does the temperature change? Explain.
The water turns into steam at 100o C
11/12/2018
Physics 214 Summer 2017

27. Q21 An ideal gas is compressed without allowing any heat to flow into or out of the gas. Will the temperature of the gas increase, decrease, or remain the same in this process?
The temperature will increase ΔU = W
Q23 Heat is added to an ideal gas, and the gas expands in the process. Is it possible for the temperature to remain constant in this situation?
Yes. This is an isothermal expansion and W = Q
11/12/2018
Physics 214 Summer 2017

28. Q25 Heat is added to a hot-air balloon causing the air to expand
Q25 Heat is added to a hot-air balloon causing the air to expand. Will this increased volume of air cause the balloon to fall?
Archimedes principle states that the buoyant force is equal to the weight of liquid displaced. So if the balloon stays the same size and as the air expands it leaves the balloon it will rise faster because the weight of the air inside will be less. If no air escapes but the balloon increases in size it will also rise because the buoyant force is larger
Q27 A block of wood and a block of metal have been sitting on a table for a long time. The block of metal feels colder to the touch than the block of wood. Does this mean that the metal is actually at a lower temperature than the wood?
No. What you feel is heat flow and the thermal conductivity of metal is much bigger than that of wood. This is also why you feel much colder when the air is damp and why trapped dry air in fiberglass is used for insulation. It is also because room temperature is lower than body temperature
11/12/2018
Physics 214 Summer 2017

29. Ch 10 E 2 Temperature is 14° F. What is the temperature in Celsius?
Tc= 5/9 (TF – 32) = 5/9 ( )=5/9 (-18) = -10° C
11/12/2018
Physics 214 Summer 2017

30. Ch 10 E6
How much heat does it take to raise the temperature of 70 g of H2O from 20°C to 80°C? C= 1 cal/gram/oC.
Q = mcT=(70)(1)(80-20) = 4200 cal
11/12/2018
Physics 214 Summer 2017

31. Ch 10 E 12 Add 600 J to 50 g of H2O initially at 20°C
How many calories?
What is the final temperature of the H2O
600 / = cal = Q
b) Q=mcT
T=Q/mc=143.3/(50)(1)=2.87°C
TF=22.87°C
11/12/2018
Physics 214 Summer 2017

32. Ch 10 E 16
Add 500 cal of heat to gas. Gas does 500 J of work on surroundings.
What is the change in internal energy of gas?
U = Q-W
Q = 500/ = 2093 J
W=500 J
U = 2093 – 500 = 1593 J
11/12/2018
Physics 214 Summer 2017

33. Ch 10 CP 2
A student’s temperature scale = 0°s = ice point of H2O; 50° s = boiling
point of H2O. The student then measures a temperature of 15°s.
What is this temperature in degrees Celsius?
What is this temperature in degrees Farenheit?
What is this temperature in Kelvins?
Is the temperature range spanned by 1°s larger or smaller than spanned by 1°C? Ts Tc
50°s
100°c
0°s
0°c
a) Ice point H2O = 0°s=0°C
Boiling point H2O = 50°s=100°C
Obvious relationship: Ts=1/2 Tc, Tc=2Ts
Tc=2Ts=2(15) = 30°C
b) TF = 9/5 Tc+ 32 = 9/5(30) + 32 = 86°F
c) Tk = Tc = = 303.2K
1°s spans 2°C, so that the range spanned by 1°S is LARGER than that
spanned by 1°C.
11/12/2018
Physics 214 Summer 2017

34. Ch 10 CP 4
150 g of metal at 120°C is dropped in a beaker containing 100 g H2O
at 20°C. (Ignore the beaker). The final temperature of metal and water is 35°C.
a) How much heat is transferred to the H2O?
b) What is the specific heat capacity of metal?
c) Use the same experimental setup – how much metal at 120°C to have final temperature of metal and water = 70°C?
a) Q = mcT = (100)(1)(35-20) = 1500 cal
Q = mcT → c = Q/mT =
c = -1500/(150)(35-120) = 0.12 cal/gram/°C
c) Q H2O = mcT = (100)(1)(70-20) = 5000 cal
Q metal = - Q H2O =
Q metal = mcT; m = Q metal/cT = -5000/(0.12)(70-120)
m = 833 g
11/12/2018
Physics 214 Summer 2017

35. Ch 11 E 6
A Carnot engine takes in heat at 650 K and releases heat to a reservoir at 350K.
What is the efficiency?
ec = (TH – Tc) / TH = / 650 = 0.46
11/12/2018
Physics 214 Summer 2017

36. Ch 11 E 8 Carnot engine operates b/w 600 K and 400 K and
does 200 J of work in each cycle.
a) What is the efficiency?
How much heat does it take in from the high-temp reservoir during each cycle?
a) εc= (TH- Tc)/TH = ( )/600 = 0.33
b) ε = W/QH , QH = W/ε = 200/0.33 = 600J
11/12/2018
Physics 214 Summer 2017

37. Ch 11 CP 2
Carnot engine operates b/w 500° C and 150° C and does 30 J of work in each cycle.
a) What is the efficiency?
b) How much heat is taking in from the high-temp reservoir each cycle?
c) How much heat is released to low-temp reservoir each cycle?
d) What is the change, if any, in the internal energy of gas each cycle?
a) εc= (TH-Tc)/ TH= ( )-( )/( ) = .045
b) ε = W/QH , QH = W/ε = 30/0.45 = 66.3 J
c) W = QH-Qc, Qc = QH-W = 66.3J - 30J = 36.3J
U = Q-W, W = 30J
Q = QH - Qc = 66.3 – 36.3 = 30 J
U = = 0
11/12/2018
Physics 214 Summer 2017