Transcript 3.1 Thermal concepts

Thermal Physics
Topic 3.1 Thermal Concepts
Temperature – Macroscopic
• At a macroscopic level, temperature is the degree of
hotness or coldness of a body as measured by a
thermometer
• Temperature is a property that determines the direction of
thermal energy transfer (heat) between two bodies in
contact
• Temperature is measured in degrees Celsius (oC) or
Kelvin (K)
– Where Temp in K = Temp in oC + 273
– Temp in K is known as the absolute temperature
DIFFERENCE BETWEEN HEAT AND THERMAL ENERGY
Thermal energy is a term often confused with that of heat.
Simply put, heat is the flow of thermal energy.
Thermal energy is the total internal energy of the system. This has to do
with the kinetic and potential energies of the molecules, i.e. how fast the
molecules are vibrating and their chemical bonds.
Heat goes from objects with high temperature to low temperature, not high
thermal energy to low thermal energy.
For example, a massive glacier will have more total thermal energy than a small
hot nail (simply because it has more molecules); however, its temperature is
lower because it has less average thermal energy. Therefore, energy will be
transferred from the nail to the glacier...
Heat will not flow between two bodies of the same temperature
Heat transfer = energy transfer
Thermal Equilibrium
• When 2 bodies are placed in contact heat will flow from the body at
higher temp to the body with lower temp
• Until the two objects reach the same temperature
• They will then be in Thermal Equilibrium
• This is how a thermometer works
Cold milk
Light
Hot black coffee
brown coffee
Thermometers
• A temperature scale is constructed by taking two fixed,
reproducible temperatures
• The upper fixed point is the boiling point of pure water at
atmospheric pressure
• The lower fixed point is the melting point of pure ice at
atmospheric pressure
• These were then given the values of 100 oC and 0 oC
respectively, and the scale between them was divided by
100 to give individual degrees
Temperature - Microscopic
▪ At a microscopic level, temperature is regarded as a measure of the
average kinetic energy per molecule (associated with its movement
in the substance)
Internal Energy
▪ Is the total potential and kinetic energy of the molecules in a substance.
• Potential energy is associated with intermolecular forces.
(arises from the bonds between molecules)
• Kinetic energy includes both translational and rotational motion.
Heat
• Heat represents energy transfer due to a temperature difference
• Occurs from higher to lower temperature regions
Methods of Heat Transfer
• Heat can be transferred from one body to another by
– Conduction (Heat transfer through material)
– Convection (Heat transfer by movement of hot material)
– Radiation (Heat transfer by light)
Conduction of heat
• Conduction in solids
– Heat energy causes atoms to vibrate, a vibrating atom passes this
vibration to the next
• Conduction in metal
– Heat energy causes electrons to gain energy, electrons travel
through metal (conduction) and carry heat energy with them
• Metals are good conductors of both heat and electricity
• The atoms at the bottom
are at a higher
temperature and will
oscillating more strongly
than those at the top.
Convection of heat
• “Hot air rises” (and takes its heat with it!)
– Radiators
• “Hot air rises” (and takes its heat with it!)
– Cumulus clouds
Convection of heat
Alternating
Land
and
Sea Breezes
Hurricanes
Plate tectonics
Radiation of heat
• involves the generation and absorption of photons. Unlike
conduction or convection, however, radiation requires no
intervening medium to transport the heat.
• All objects radiate energy continuously in the form of
electromagnetic waves
• The hotter an object the more
power it radiate sand the shorter
the wavelength of the peak
emission wavelength
Are heat emitter also good absorbers?
• Black and dull on the surface
– Best emitter/absorber
– Charcoal
– Blackbody radiators
• perfect absorber & emitter
• White and polished/shiny
– Good Reflectors
– Stay cool in the summer
The Thermos Bottle
Discuss the operation of a thermos making reference to methods of
heat exchange.
The “colour” of heat
• Peak wavelength of light emitted depends on temperature
• Spectrum includes all wavelength longer than the peak but not many above
– 20°C - peak in infrared (need thermal imaging camera to see body heat)
– 800°C - peak in red (electric coil, fire glows reds)
– 3000° - peak in blue (but includes green and red light hence appears
white)
– 2.7K peak in micro-wave (background emission in the universe left over
from the Big Bang)
Thermal Physics
Topic 3.2 Thermal Properties of
Matter
Heat Capacity/Thermal Capacity, C
● When different substances undergo the same temperature change
they can store or release different amounts of energy
● they have different heat capacities
● HEAT CAPACITY is the amount of energy required to raise the
temperature of a substance/body by 1K
𝑄
𝐶=
𝐽𝐾 −1
∆𝑇
• Q = amount of thermal energy in joules
•T = change in temperature in Kelvins
● Applies to a specific BODY
•
A body with a high heat capacity will take in thermal energy at a slower rate than a
substance with a low heat capacity because it needs more time to absorb a greater
quantity of thermal energy
•
They also cool more slowly because they give out thermal energy at a slower rate
Specific Heat Capacity, c
• Specific Heat Capacity is the amount of thermal energy required
to raise temperature of 1 kg of a substance by one Kelvin
• Specific Heat Capacity =
𝑄
𝐶=
𝑚∆𝑇
𝐽𝑘𝑔−1 𝐾 −1
where m is the mass of the material
• For an object made of one specific material:
Heat Capacity = m × Specific Heat Capacity
• Unit masses of different substances contain
– different numbers of molecules
– of different types
– of different masses
• If the same amount of internal energy is added to each unit mass
– it is distributed amongst the molecules
• The average energy change of each molecule will be different for each
substance
• Therefore the temperature changes will be different
• So the specific heat capacities will be different
Heat Capacity
Whereas ‘specific’ heat capacity is ‘per kg’ of a material, heat capacity (or
thermal capacity) is the energy required to raise a certain objects
temperature by one Kelvin, irrespective of its mass.
Heat capacity = mass x specific heat capacity
C = mc
m = mass (kg)
C = heat capacity (JK-1)
c = specific heat capacity(Jkg-1K-1)
∆T = Change in temp (K)
∆Q = Amount of heat energy (J)
Amount of energy needed to raise temperature of an object by ∆T K is
∆Q = C∆T
Amount of energy needed to raise temperature of 1 kg of a substance by ∆T K is
∆Q = cm∆T
The same amount is released if the temperature decreases
● Zeroth law of thermodynamics – If two thermodynamic systems are each in
thermal equilibrium with a third, then they are in thermal equilibrium with each other.
● First law of thermodynamics – Energy can neither be created nor destroyed. It can
only change forms. In any process, the total energy of the universe remains the
same. For a thermodynamic cycle the net heat supplied to the system equals the net
work done by the system.
Sir James Joule
1st law of thermodynamics:
heat and work are both forms of energy
Stirring water made it warm
Change in temperature proportional to work done
Showing equivalence of heat and mechanical energy
Also that electrical current flow through a resistor causes heating
Applying all these to problems:
PROBLEMS:
1. A 2.00-kg metal object requires 5.02 x 103 J of heat to raise its temperature from
20.0 °C to 40.0 °C. What is the specific heat capacity of the metal?
126 J/(kg • C°)
2. A 0.20-kg lead shot is heated to 90.0 °C and dropped into an ideal
calorimeter containing 0.50 kg of water initially at 20.0 °C. What is the final
equilibrium temperature of the lead shot? The specific heat capacity of lead
is 128 J/(kg • C°); and the specific heat of water is 4186 J/(kg • C°).
20.8 °C
3. Given that the specific heat capacity of water is 11 times that of copper, calculate
the mass of copper at a temperature of 100 °C required to raise the temperature of
200 g of water from 20.0 °C to 24.0 °C, assuming no energy is lost to the
surroundings.
4. Three litres of water at 100 °C are added to 15 litres of water at 40 °C. Calculate
the temperature of the mixture. Take the mass of 1 litre of water to be 1 kg and the
specific heat capacity of water to be 4.2 × 103 J kg -1 K -1
5. A heater of 800W is use to heat a 600 g cast iron cooker plate.
How long will it take to raise the temperature of the plate by 200 oC?
Specific heat capacity of iron = 500 J/(kg K)
Pt = m c T
or
V I t = m c T
75 s = 1 minute 15 s
6. A hole is drilled in an 800g iron block and an electric heater is placed inside.
The heater provides thermal energy at a constant rate of 600 W.
a) Assuming no thermal energy is lost to the surrounding environment, calculate
how long it will take the iron block to increase its temperature by 150 C.
9.0 s
b) The temperature of the iron block is recorded as it varies with time and is
shown at right. Comment on reasons for the shape of the graph.
begins at room temp
increases linearly as Q = cmΔT
as gets hotter, more energy lost to environment
levels out when heat gained by heater = heat lost to room
c) Calculate the initial rate of increase in temperature.
1.7 0C/s
Example of finding c of a liquid using electrical current
•
Using a calorimeter of known heat capacity
Stirrer
To voltmeter
and ammeter
Thermometer
Calorimeter
•
•
•
•
•
Electrical energy = V I t
Energy gained by liquid = ml cl Tl
Energy gained by calorimeter = mc cc Tc
Using conservation of energy
Electrical energy input =
thermal energy gained by liquid
+ thermal energy gained by calorimeter
•
V I t = ml cl Tl + mc cc Tc
•
The only unknown is the specific heat
capacity of the liquid
Heating coil
Liquid
Insulation
Example of finding c of a solid using electrical
current
•
•
Using a specially prepared block of the material
The block is cylindrical and has 2 holes drilled in it
– one for the thermometer and one for the heater
– Heater hole in the centre, so the heat spreads evenly through the block
– Thermometer hole, ½ way between the heater and the outside of the block,
so that it gets the averge temperature of the block
•
V I t = ms cs Ts
•
The only unknown is the specific heat
capacity of the solid
Method of mixtures
•
Sometimes called the method of mixtures
•
In the case of solid, a known mass of solid is heated to a known temperature
(usually by immersing in boiling water for a period of time)
•
Then it is transferred to a known mass of liquid in a calorimeter of known mass
•
The change in temperature is recorded and from this the specific heat
capacity of the solid can be found
•
Energy lost by block = Energy gained by liquid and calorimeter
•
mb cb Tb = mw cw Tw + mc cc Tc
– the SHC of water and the calorimeter are needed
Phases (States) of Matter
•
•
•
•
•
Matter is defined as anything that has mass and occupies space
There are 4 states of matter
Solids, Liquids, Gases and Plasmas
Most of the matter on the Earth in the form of the first 3
Most of the matter in the Universe is in the plasma state
Macroscopic properties
• Macroscopic properties are all the observable behaviours of that
material such as shape, volume, compressibility
• The many macroscopic or physical properties of a substance
can provide evidence for the nature of that substance
Macroscopic
Characteristics
Microscopic
Characteristics
Fluids
•
•
•
•
Liquids
Gases
are both fluids
Because they FLOW
Arrangement of Particles
• Solids
• Closely packed
• Strongly bonded to neighbours
• held rigidly in a fixed position
• the force of attraction between particles gives them PE
• Liquids
• Still closely packed
• Bonding is still quite strong
• Not held rigidly in a fixed position and bonds can break and reform
• PE of the particles is higher than a solid because the distance
between the particles is higher
• Gases
• Widely spaced
• Only interact significantly on closest approach or collision
• Have a much higher PE than liquids because the particles are furthest apart
Changes of State
•
A substance can undergo changes of state or phase changes at different temperatures
•
Pure substances have definite melting and boiling points which are characteristic of the
substance
– When the solid is heated the particles of the solid vibrate at an increasing
rate as the temperature is increased
– The vibrational KE of the particles increases
– At the melting point a temperature is reached at which the particles vibrate
with sufficient thermal energy to break from their fixed positions and begin
to slip over each other
– As the solid continues to melt more and more particles gain sufficient
energy to overcome the forces between the particles and over time all the
solid particles are changed to a liquid
– The PE of the system increases as the particles move apart
– (actually it absolutely decreases towards zero)
– As the heating continues the temperature of the liquid rises due to an increase in the
vibrational, rotational and translational energy of the particles
– At the boiling point a temperature is reached at which the particles gain sufficient
energy to overcome the inter-particle forces and escape into the gaseous state. PE
increases.
– Continued heating at the boiling point provides the energy for all the particles to
change
Heating Curve
Temp / oC
Liquid - gas
phase change
Solid - liquid
phase change
Time /min
Changes of State
Thermal energy added
sublimation
Deposition/desublimation
Melting/fusion
SOLID
vaporisation
LIQUID
Freezing/solidification
GAS
condensation
Thermal energy given out
Mom melted chocolate and poured it into molds. She then put it in the fridge to
cool. She left it overnight, so it stayed in the fridge even after the chocolate became
hard. Which graph best shows the temperature of the chocolate while in the fridge?
Latent Heat
•
The thermal energy absorbed or released in phase change is called
Latent Heat because it does not produce a change in temperature
There is no temperature change during a phase change, thus there is no change in
the kinetic energy of the particles in the material. The energy released/absorbed
comes from the potential energy stored in the bonds between the particles.
•
Thermal energy absorbed by a body results in decrease of PE of the particles
as they move closer together
•
Thermal energy released by a body, increases PE of the particles as they move
further apart move further apart
NONSENSE
Latent heat is the thermal energy absorbed or released by a body
during a change of phase (at constant pressure).
L = Qat const. P
unit: J
Specific latent heat is the thermal energy required to change the
phase of 1 kg of a substance (at constant pressure).
L=
Q
m
→
Q = mL
unit: (L) = J/kg
Types of Latent Heat
• Fusion
• Vaporisation
• Sublimation
• The latent heat of fusion of a substance is less than the latent heat
of vaporisation or the latent heat of sublimation
Methods of finding Latent Heat
• Using similar methods as for specific heat capacity
• The latent heat of fusion of ice can be found by adding ice to water
in a calorimeter
•
•
•
•
Block
of ice
The change in temperature is recorded and
from this the latent heat of fusion of the ice
can be found
Energy gained by block melting = Energy
lost by liquid and calorimeter
mb Lb = mw cw Tw + mc cc Tc
the SHC of water and the calorimeter are
needed
Thermometer
Calorimeter
Water
Block of ice
Insulation
Latent Heat of Vaporisation
•
•
•
•
•
•
•
•
The initial mass of the liquid is recorded
The change in temperature is recorded for heating the liquid to boiling
The liquid is kept boiling
The new mass is recorded
Energy supplied by heater = energy to raise temperature of liquid
+ energy use to vaporise some of the liquid
(The calorimeter also needs to be taken in to account.
V I t = ml clTl+ me Le + mc ccTc
Scattered thoughts …
• Under extreme conditions of heat and exercise, an individual may sweat more
than a liter of liquid per hour.
• The interior of roasted meat can never reach temperatures higher than the
boiling point of water until all the water is cooked out of it, at which point it would
resemble shoe leather. The outside is quickly dried out, however, and can reach
the temperature of the surrounding cooking medium.
• Cocoa butter is unique among the fats in that it is very regular in composition;
whereas most other fats are actually mixtures. This gives it a very definite point;
unlike butter, which softens gradually. As it melts in your mouth, it absorbs latent
heat. This makes chocolate bars taste "cool". Cocoa butter is remarkably uniform
in composition and structure: only three fatty acids in the majority of its
triglycerides, with the same one occupying the middle position. Pure cocoa butter
is quite brittle up to about 34 ℃ (93 ℉), at which point it melts quite quickly.
Changes in size:
An increase in temperature generally causes bodies to expand, while a reduction in
temperature causes bodies to contract.
Engineers must take expansion into account when they are designing various
structures (bridges,…).
When concrete roads are laid down, gaps (normally filled with tar) are left between
sections in order to allow for expansion.
Why do solids expand with increasing temperature?
The atoms or molecules in a solid vibrate at all temperatures above the absolute
zero. As the temperature increases, the vibrations increase in amplitude, and this
pushes the atoms further apart. This occurs in all three dimensions.
Why do liquids expand with increasing temperature?
As the temperature increases, the kinetic energy of the
molecules of the liquid increases. The movement of the molecules gradually
overcomes forces of attraction between the molecules, with the result that they have
greater freedom to move, over greater volumes. Thus the liquid expands.
Water behaves in an anomalous manner. It contracts as the temperature
increases from 0 ºC to 4 ºC, reaching its highest density at that temperature.
This has enormous significance for aquatic life in regions with severe winters.
The abnormal behaviour of water:
At 4 ºC, water has its highest density. It actually contracts as
the temperature rises from 0 ºC to 4ºC. This means that in
regions with severe winters, lakes cool at the surface, and when the surface water
reaches 4 ºC, that water, being more dense, sinks. A temperature gradient is set up,
and when the water freezes, it does so at the surface. Eventually, the ice, which floats
on water, acts as an insulator, protecting the water below it from further cooling.
This results in lakes freezing from the top down, and not from the bottom up. This
means that fishes can survive below the ice even if the air temperature is far below
0 ºC for prolonged periods. The reason for this anomalous behaviour of water is
beyond the scope of the IB Physics curriculum.
Q. Explain why supply of latent heat causes a change in potential energy
but not kinetic energy.
A. Kelvin temperature is proportional to the KE of the molecules.
Thus if the temperature hasn’t increased then the KE has also not increased.
Work has been done against forces, changing the position of the molecules. Thus the
PE of the molecules must change.
EXAMPLE: Let:
i. Specific latent heat of vaporisation (Lv) - from liquid to vapour
ii. Specific latent heat of fusion (Lf) - from solid to liquid
Then if 0.5kg of ice at 0°C is heated…
i. … until it has all melted to water at 0°C
ii. … until it reaches it’s boiling point at 100°C
iii. … until it has vaporised to steam at 100°C
Calculate the heat supplied at each stage and in total.
∆Q = mLv
∆Q = mLf
∆Q = Amount of heat energy (J)
L = Specific latent heat (Jkg-1)
m = mass (kg)
A
i. ΔQ
= mLf
= 0.5 x 334 x 103
= 1.67 x 105 J
ii. ΔQ
= mcΔT
= 0.5 x 4200 x 100
= 2.10 x 105 J
iii.ΔQ
= mLv
= 0.5 x 2258 x 103
= 1.13 x 106 J
Total = 1.51 x 106 J ( = 1.51 MJ)
Example: Which one of the following statements is UNTRUE?
1. Impurities generally decrease the melting point of substances.
2. Water can boil at room temperature.
3. Ice does not evaporate.
4. Steam may attain temperatures above 100 ºC.
5. The melting point of ice decreases with increasing pressure.
3. is correct. A great many solids, including ice, can evaporate without
having first to turn into a liquid. This process is called SUBLIMATION.
Example: An iceberg has a mass of 10 000 tons.
How much heat will be required to melt the iceberg
(initially at 0 ºC) and bring the resulting water to a to
a temperature of 6 ºC? (Take the specific heat
capacity of water as 4.2 kJ.kg-1.ºC-1 and the specific
latent heat of fusion of ice as 334 kJ.kg-1.)
Heat required = Heat to melt the iceberg + heat to raise the water temperature
Heat required to melt the iceberg = mass of iceberg x latent heat of fusion of ice
= 10000 (tons) x 1000 (kg.ton-1) x 334 (kJ.kg-1)
= 3.34 x 109 kJ.
Heat required to raise the water temperature
= mass of water x specific heat capacity x temperature rise
= 1.0 x 107 (kg) x 4.2 (kJ.kg-1.ºC-1) x 6 (ºC)
= 2.52 x 108 kJ
Total heat = 3.34 x 109 kJ + 2.52 x 108 kJ = 3.6 x 109 kJ = 3.6 x 106 MJ
Example: An immersion heater supplies heat at a rate of 5 J.s-1 to an
insulated vessel containing a certain liquid. The liquid was brought to its
boiling point and kept boiling for 2 minutes, during which time the liquid
lost 4.0 g. What value for the specific latent heat of vaporization of the
liquid can be calculated from this experiment?
We assume that the heat supplied by the heater is the heat
required to convert 4.0 g of the liquid at its boiling point to the
vapour state.
P t= m L
5 (J.s-1) x 120 (s) = 4.0 (g) x specific latent heat (J.g-1).
The specific latent heat = 5 (J.s-1) x 120 (s)/4.0 (g)
= 150 J.g-1
Example: A certain substance is heated at a constant rate, and its temperature
measured as a function of time. The graph of the results obtained is shown in
the diagram below. Which one of the following statements is FALSE?
1. No liquid exists in the region labelled A
2. Region C involves the heating of a liquid only
3. No liquid exists in the region labelled B
4. No solid exists in the region labelled D
5. Region E involves the heating of a gas only
4. Correct. The statement is FALSE.
In the flat region labelled B, latent heat of fusion is
absorbed without a change in temperature. The substance
is melting, thus both solid and liquid are present
Example: Calculate the amount of heat required to completely convert 50 g of ice at
0 ºC to steam at 100 ºC. The specific heat capacity of water is 4.18 kJ.kg-1.K-1.
The specific latent heat of fusion of ice is 334 kJ.kg-1, and the specific heat of
vaporization of water is 2260 kJ.kg-1.
5. Answer: Heat is taken up in three stages: 1. The melting of the ice, 2. the heating
of the water, and 3. the vapourization of the water. The heat taken up in the complete
process is the sum of the heat taken up in each stage.
Heat taken up for converting ice at ºC to water at ºC
mass of water x latent heat of fusion = 0.050 (kg) x 334 (kJ.kg-1) = 16.7 kJ
Heat taken up heating the water from 0 ºC to the boiling point, 100 ºC
mass of water x specific heat capacity x temperature change
= 0.05 (kg) x 4.18 (kJ.kg-1. K-1)x 100 (º K) = 20.9 kJ
Heat taken up vapourizing the water
mass of water x latent heat of vaporization = 0.05 (kg) x 2260 kJ.kg-1 = 113 kJ
The sum of these is
16.7 + 20.9 + 113 = 150.6 kJ (151 kJ)
Evaporation
• The process of evaporation is a change from the liquid state to the
gaseous state which occurs at a temperature below the boiling point
Explanation
• A substance at a particular temperature has a range of particle energies
• So in a liquid at any instant, a small fraction of the particles will have KE
considerably greater than the average value
• If these particles are near the surface of the liquid, they will have
enough KE to overcome the attractive forces of the neighbouring
particles and escape from the liquid as a gas
• This energy is needed as gases have more PE than liquids.
Cooling
• Now that the more energetic particles have escaped
• The average KE of the remaining particles in the liquid will be
lowered
• Since temperature is related to the average KE of the particles
• A lower KE infers a lower temperature
Cool
• This is why the temperature of the liquid falls as an evaporative
cooling takes place
• A substance that cools rapidly is said to be a volatile liquid
• When overheating occurs in a human on hot days, the body
starts to perspire
• Evaporation of the perspiration cools the body
Factors Affecting The Rate
• Evaporation can be increased by
– Increasing temperature
– (more particles have a higher KE)
– Increasing surface area
– (more particles closer to the surface)
– Increasing air flow above the surface
– (gives the particles somewhere to go to)