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Chapter 10: Basic Physics SE-Heat

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The Big Ideas

Heat is a form of energy transfer. Materials do not contain heat. They contain internal energy that can be transferred (i.e. heat) from one body to another. Internal energy is the vibrating and rotating and general jostling of atoms and/or molecules that make up the ‘thing,’ whether it is wood, steel, water. One way to measure the heat of an object is to measure its temperature. This is really a statement about its internal kinetic energy.

Heat expansion is a result of the increase of kinetic energy of the molecules. As their movement increases, they bump into each other more and the material slightly expands as a result. Most materials expand with heat. Water is a particularly interesting substance in that it contracts as its temperature increases from 0^\circ C to 4^\circ C (and then expands from 4^\circ C to 100^\circ C).

Heat can be transferred in three ways, through conduction, convection, and radiation. Conduction is the transfer of heat by physical contact. Heat flows form the hotter object to the cooler object. Convection is heat transfer by an intermediate substance (for example air or water). Your oven (often properly called the ‘convection oven’) works by heating up the air and then the air heats up your food. Radiation is the release of heat (and thus the lowering of its internal energy) by releasing electromagnetic waves. The hotter the object the higher the frequency of the light emitted. When you look at a fire the blue flames our hotter than the red flames because blue has a higher frequency than red.

Entropy is a measure of disorder, or the variety of ways in which a system can organize itself with the same total energy. The entropy of any isolated system always tends to disorder (i.e. entropy is always increasing). In the universe, the entropy of a subset (like evolution on Earth) can decrease (i.e. more order), but the total entropy of the universe is decreasing (i.e. more disorder).

Key Concepts

  • When an object feels cold to the touch, it is because heat is flowing from you to the object.
  • When an object feels hot to the touch, it is because heat is flowing from the object to you.
  • Some objects (like metals) conduct heat better than others (like wood). Thus if you stick a metal rod in the fireplace and hold the other end, the heat is conducted well and you get burned. On the other hand, if you place a wood stick in the fire and hold the other end you’ll be OK.
  • The temperature of a gas is a measure of the amount of average kinetic energy that the atoms in the gas possess.
  • If you heat something, you increase its internal energy, so you increase the movement of molecules that make up this thing, thus it expands. This is called heat expansion; most everything expands as heated and contracts as cooled.
  • Most materials expand as they are heated. This can cause bridges to collapse if they are not designed to have a place to expand in the summer months (like the placing of metal ‘teeth’ at intervals on the Golden Gate Bridge).
  • Water contracts from 0^\circ C to 4^\circ C and then expands from 4^\circ C to 100^\circ C. Remembering that density is mass divided by volume explains why water at 4^\circ C is more dense than water below and above 4^\circ C. This also explains why lakes freeze on the top first and not throughout. As the water on the top of the lake drops below 4^\circ C, it is now more dense than the water below it, thus it sinks to the bottom, allowing the warmer water to rise up to the top and cool down in the winter weather. Only when the entirety of the lake is at 4^\circ C, then the lake can start to freeze. It freezes from the top down, because water below 4^\circ C is less dense than water at 4^\circ C.

  • There are 3 different temperature scales you should know-the Kelvin scale, the Celsius scale and the Fahrenheit scale.
  • The Kelvin scale (K) is the one used in most scientific equations and has its zero value set at absolute zero (the theoretical point at which all motion stops).
  • The Celsius scale (^\circ C) is the standard SI temperature scale. It is equal to the Kelvin scale if you minus 273 from the Celsius reading. Water has a boiling point of 100^\circ C and a freezing point of 0^\circ C.
  • The Fahrenheit scale (^\circ F) is the English system and the one we are familiar with.
  • Newtons’ Law of Cooling: The rate of heat transfer is proportional to the difference in temperature between the two objects. For example, hot liquid that is put in the freezer will cool much faster than a room temperature liquid that is put in the same freezer.
  • Heat capacity is the amount of internal energy that the substance can store. A large heat capacitance means the substance can store a lot of internal energy and thus the temperature changes slowly. Aluminum foil has a small heat capacitance and water has a large one.
  • The amount of heat capacitance (and thus its specific heat value) is related to something called ‘degrees of freedom,’ which basically says how free is the object to move in different ways (and thus how much kinetic energy can it store inside itself without breaking apart). For example, solids have a more fixed structure, so they cannot rotate and jostle as much, so they can’t store as much internal energy so they have lower heat capacitance then liquids.
  • Specific heat is similar to heat capacitance, but is a specific number. The specific heat tells you how much energy one must put in per unit mass in order to raise the temperature 1^\circ C.
  • Phase changes: it takes energy to changes phases from a solid to a liquid and from a liquid to a gas. The substance releases energy when changing phase from gas to liquid or from liquid to solid. How much energy per unit mass depends on the substance in question. When you get out of the shower you often feel cold. This is because the water on you is evaporating, and heat is flowing from you to the water droplets in order for them to change phase from water to gas. You are losing heat and thus feel cold.

Key Application

  • The human body radiates heat in the range of infrared light. Night goggles work by ‘seeing’ the infrared light emitted by our bodies.

  • The thermostat works with a bi-metallic strip. A bi-metallic strip is a flat rectangular object with two different metal strips glued together back to back. In the example above (courtesy of ‘hyperphysics’) we have brass and steel. Brass has a larger heat expansion than steel. When the temperature gets Hotter, the brass strip will expand more than the steel one and thus the strip will bend downward, triggering the thermostat to turn on the air conditioner. When the Temperature goes below the set value, then the brass one contracts more than the steel one and it bends upward. This triggers the heating to be turned on.
  • A calorie is a unit of energy. The food Calorie, with a capital C, is actually 1,000 calories (a kcal). Thus, for example, a snicker bar labeled with 200 Cal is actually 200,000 cal.
  • Food calories are determined by burning the food and measuring the heat released.
  • The human body is at a temperature that radiates away heat in the form of infrared wavelengths. Night goggles work by ‘seeing’ the infrared light and then converting it into visible light (the green screen you usually see in the movies is because the conversion is usually done with a phosphorous screen).
  • For electronics in space, one must use very large heat sinks to radiate away the heat from components and chips like the processor. Since there is no air in space, a fan will not do anything. The processor chip cannot release heat built up by convection, so it must radiate it away over a large heat sink.
  • More than 50% of the water rise expected from global warming is due to the thermal expansion of water (more on greenhouse effect below).

The Greenhouse Effect

Greenhouse Effect: The solar energy reaching the surface of the Earth is concentrated in short wavelengths, which can easily penetrate the greenhouse gases, such as carbon dioxide and methane. The Earth, however, is cooler than the sun and it radiates its heat in the form of energy in the far infrared range. These longer wavelengths are partially absorbed by the greenhouse gases and some of the solar heat is returned to Earth. At a certain temperature these processes are in equilibrium and the surface temperature of the Earth is stable. However, if more greenhouse gases are put in the atmosphere the amount of trapped terrestrial radiation increases, leading to an increase in global temperature.

Current Situation: Currently the heating effect of extra greenhouse gases (since the start of the industrial revolution) is equal to about 1.0 \ W/m^2. Thus the recent period has recorded parallel increases in concentration of carbon dioxide and average global temperature. As more greenhouse gases are put into the atmosphere the temperature will increase further. There are certain effects of a warmer Earth (discussed more in optional section), which could accelerate the process, even if no more greenhouse gases are put into the atmosphere (an unlikely prospect for the foreseeable future).

Possible Effects That Can Accelerate Global Warming:

  1. Time Lag: The excess energy warms the ocean very slowly, due to water’s high heat capacity. Even in the unlikely event that no more greenhouse gases are added to the atmosphere the temperature increase already measured will be almost doubled.
  2. The Effect of Water Vapor: Increasing temperatures will lead to more evaporation and more water vapor in the atmosphere. Water vapor is a greenhouse gas and its increased presence may cause further warming in a positive feedback loop. On the other hand if the water vapor results in more clouds more solar radiation will be reflected, a possible negative feedback.
  3. Albedo is the amount of light reflected by a surface. Sea ice has an albedo of .85, meaning 85% of light is reflected back from its surface (and leaves the Earth) and 15% is absorbed and stays in the Earth; ice-free water has an albedo of .07. (93% of the solar energy is absorbed.) Thus the observed melting of sea ice could amplify the effect of global warming
  4. The Melting of the Artic Permafrost also has an amplifying effect by releasing carbon dioxide and methane that is normally trapped in the tundra.
  5. Warmer oceans are hostile to algae and cytoplankton, which are the most important absorbers of carbon dioxide. The loss of these two photosynthesizers would remove the most important natural CO_2 sink.
  6. Loss of Rain Forests would have a similar effect. Global warming is likely to lead to desertification of the habitats of rain forests. The rain forest is the second most important CO_2 sink.

Key Equations

  •  T_F = \frac{9}{5}T_C + 32^\circ \text{F} ; conversion from Celsius to Fahrenheit
  •  T_C = \frac{5}{9}(T_F - 32^\circ \text{F}) ; conversion from Fahrenheit to Celsius
  • Q = mc \Delta T ; the heat gained or lost is equal to the mass of the object multiplied by its specific heat multiplied by the change of its temperature.
  • Q = mL ; the heat lost or gained by a substance due to a change in phase is equal to the mass of the substance multiplied by the heat of vaporization/fusion
  • 1 cal = 4.184 Joules ; your food calorie is actually a kilocalorie (Cal) and equal to 4184 J.
Table of Specific Heat Values
Substance Specific Heat, c (cal/g^\circ C)
Air 6.96
Water 1.00
Alcohol 0.580
Steam 0.497
Ice (-10^\circ C) 0.490
Aluminum 0.215
Zinc 0.0925
Brass 0.0907
Silver 0.0558
Lead 0.0306
Gold \sim Lead 0.0301
Table of Heat of Vapourization
Substance Fusion, L_f (cal/g) Vaporization, L_v (cal/g)
Water 80.0 540
Alcohol 26 210
Silver 25 556
Zinc 24 423
Gold 15 407
Helium - 5.0

Heat Problem Set

  1. A sandy beach can be very cool at night but on a hot day can be too hot to walk across barefoot! Does the sand have a HIGH or LOW specific heat capacity? Explain briefly.
  2. Draw the density curve of water below.
  3. Why is San Francisco always around the same temperature all year, where as Washington DC has very cold winters and very hot summers?
  4. A thermometer measures its own temperature. Why is this so, and why does it also give you the temperature of say the hot coffee you stick it in?
  5. Temperature is a measure of the average kinetic energy of molecules. Consider a mixture of hydrogen and oxygen gas at a certain temperature. Use the formula for kinetic energy to explain why the hydrogen molecules move faster than the oxygen molecules. Then explain why there’s no hydrogen in the earth’s atmosphere, and why the moon has no atmosphere at all.
  6. Why are icebergs often surrounded by fog?
  7. Why should you not pick up a hot pan with a wet cloth?
  8. Explain how a bimetallic switch can be used as a switch in a thermostat to turn a furnace on and off. Use a diagram in your explanation.
  9. One object is radiating UV light and one is radiating IR light. Which is hotter and why?
  10. Why is a blue flame hotter than a red flame?
  11. On the outside of some houses the water pipes are wrapped in insulating material. This is particularly common in the Midwest and North. Explain.
  12. Walking on hot coals in sometimes touted as an example of “mind over matter”... give a physics explanation for why it is possible to walk (quickly) over red-hot coals. Why is it even easier to do this after the coals have been burning for a couple of hours?
  13. A regular convection oven and a microwave both heat up the food. But they use different methods to transfer heat into the food, what are they?
  14. A wood bar and a metal bar are both at room temperature. Which will feel colder? Why?
  15. Ocean breeze comes off the ocean on a hot day (on shore breeze), why? Use a diagram as part of your explanation.
  16. Explain why a lake freezes at the top first, rather than throughout or at the bottom?
  17. Why is it so cold when you get out of the shower wet, but not as cold if you dry off first before getting out of the shower?
  18. You are going to drink your freshly poured and hot coffee in exactly 5 minutes. You like milk in your coffee and you want your coffee to be as hot as possible when you drink it. Should you pour the milk in now or right before drinking it? Explain.
  19. Antonio is heating water on the stove to boil eggs for a picnic. How much heat is required to raise the temperature of his 10.0-kg vat of water from 20^\circ C to 100^\circ C?
  20. Amy wishes to measure the specific heat capacity of a piece of metal. She places the 75-g piece of metal in a pan of boiling water, then drops it into a styrofoam cup holding 50 g of water at 22^\circ C. The metal and water come to an equilibrium temperature of 25^\circ C. Calculate:
    1. The heat gained by the water
    2. The heat lost by the metal
    3. The specific heat of the metal
  21. John wishes to heat a cup of water to make some ramen for lunch. His insulated cup holds 200 g of water at 20^\circ C. He has an immersion heater rated at 1000 W (1000 J/s) to heat the water.
    1. How many JOULES of heat are required to heat the water to 100^\circ C?
    2. How long will it take to do this with a 1000-W heater?
    3. Convert your answer in part b to minutes.
  22. You put a 20g cylinder of aluminum (c=0.2 \ cal/g/^\circ C) in the freezer (T=-10^\circ C). You then drop the aluminum cylinder into a cup of water at 20^\circ C. After some time they come to a common temperature of 12^\circ C. How much water was in the cup?
  23. Emily is testing her baby’s bath water and finds that it is too cold, so she adds some hot water from a kettle on the stove. If Emily adds 2.00 kg of water at 80.0^\circ C to 20.0 kg of bath water at 27.0^\circ C, what is the final temperature of the bath water?
  24. You are trying to find the specific heat of a metal. You heated a metal in an oven to 250^\circ C. Then you dropped the hot metal immediately into a cup of cold water. To the right is a graph of the temperature of the water versus time that you took in the lab. The mass of the metal is 10g and the mass of the water is 100g. Recall that water has a specific heat of 1 \ cal/g^\circ C.
  25. How much heat is required to melt a 20 g cube of ice if
    1. the ice cube is initially at 0^\circ C
    2. the ice cube is initially at -20^\circ C (be sure to use the specific heat of ice)
  26. A certain alcohol has a specific heat of 0.57 \ cal/g^\circ C and a melting point of -114^\circ C. You have a 150 g cup of liquid alcohol at 22^\circ C and then you drop a 10 g frozen piece of alcohol at -114^\circ C into it. After some time the alcohol cube has melted and the cup has come to a common temperature of 7^\circ C
    1. What is the latent heat of fusion (i.e. the ‘L’ in the Q = mL equation) for this alcohol? 
    2. Make a sketch of the graph of the alcohol’s temperature vs. time  
    3. Make a sketch of the graph of the water’s temperature vs. time
  27. Due to the greenhouse effect, we currently have an estimated energy imbalance of 1 W/m^2. In other words, the Earth is absorbing 1J per second for every m^2 of area.
    1. How many joules of energy is the surface of the Earth taking in every second (you may need to look up the radius of Earth)?
    2. What mass of ice can be melted by this much energy over the course of one year?
    3. What volume of water will that add to our oceans? (recall the density of water is 1000 \ kg/m^3)?
    4. From the above result and a little research on the surface area of the oceans on Earth, what would the increase in ocean levels be for one year? For the next 10 years?
    5. How would these results change if the energy imbalance increases over the next 10 years to 5 \ W/m^2 (so take the average of 3 \ W/m^2)?
  28. Explain the greenhouse effect in your own words. Talk about the positive feedback loop(s).
  29. Given the following table, involving the growth in concentration of greenhouse gases:
year [CO_2] ppm [CH_4] ppb
1940 310 1100
1960 315 1250
1980 335 1550
2000 370 1750
2020 (IPCC^* projection) 420 2150

^*Intergovernmental Panel on Climate Change

    1. Graph this data (either very carefully by hand or, better, using Excel) with time on the horizontal axis
    2. From your graph find the best fit line from in the following time periods to determine the average rate of increase in the concentrations of the two gases
      1. 1940 - 2000
      2. 1960 - 2000
      3. 1980 - 2020
  1. An overlooked area of additional global warming is the traditional cook stove. The soot smoke produced from this stove in one Honduran study absorbed 65% of terrestrial radiation that then goes into warming the atmosphere. There 400 million such cook stoves worldwide, which emit 1.5 g of soot per kilogram of wood burned. The average daily use of wood is 7.5 kg per stove. Calculate the mass of soot released through cook stoves per day, per year.
Emissions of Carbon Dioxide for Different Fuels
Fuel Kg of carbon dioxide emitted/gallon
gasoline 8.78
California reformulated gasoline, 5.7% ethanol 8.55
ethanol 6.10
Diesel #2 10.05
biodiesel 9.52
Jet fuel 9.47
propane 5.67
Natural gas/gasoline gallon equivalent 6.86
  1. Compare the carbon “footprint” of the following: 
    1.  hybrid car (45 mpg) that drives 21,000 mile per year in Calif.  
    2. A SUV (17 mpg) that drives 21,000 miles per year also in Calif. 
    3. A commercial flatbed (11 mpg) that drives 21,000 miles per year and uses bio diesel
  2. Physics Today estimates that the world’s population converts 4 \times 10^{20} \ Jof energy every year.
    1. Calculate the RATE (watts) at which that energy would be used if it’s consumed at a constant rate over one year.
    2. Estimate the world’s population and calculate the watts per person consumed. Compare that rate to the average US consumption of 12 KW per person, and the rate advocated by 2000 Watts, a group recommending that humans aim for a power consumption of no more that 2 kW per person.
    3. If all that energy used in one year went to heating water, how much water could be heated from 25^\circ C and boiled into steam?
  3. Research some typical mileages, type of fuel used, and miles covered in a year and determine the carbon footprint for:
    1. a tractor-trailer truck
    2. a commercial airliner
    3. a corporate jet
    4. a bus
    5. Amtrak
  4. A pile driver of mass 2000 kg is dropped from a height of 2.7 m onto a steel spike, driving the spike 12 cm into the ground. Calculate:
    1. the work done by the pile driver.
    2. the force exerted by the pile driver on the spike.
    3. the acceleration of the pile driver when it hits the spike.
    4. The time for the pile driver to come to rest when it hits the spike.
    5. The temperature change of the spike if all the work done by the spike were converted into heat to raise the temperature of the spike, the spike has a mass of 500 kg and the specific heat of steel is 0.45 \ J/g^\circ C.

Answers:

  1. 800,000 cal or 3360 kJ

    1. 150 cal (630 J)
    2. same as a!
    3. 0.027 \ cal/g^\circ C \ (0.11 \ J/g^\circ C)
    1. 67,000 J
    2. 67.2 s
    3. 1.1 min
  2. 11.0 g
  3. 31.8^\circ C
  4. 0.44 \ cal/g^\circ C

    1. 1600 cal (6720 J)
    2. 1800 cal (7560 J)
  5. 59.3 cal/g

    1. 5.1 \times 10^{14} J
    2. 1.5 \times 10^9 kg
    3. 1.5 \times 10^6 m^3
  1. 4.5 \times 10^9 g/day, or 1.6 \times 10^{12} g/yr

    1. 1.3 \times 10^{13} W 
    2. 1300 W/person 
    3. 1.6 \times 10^{14} kg

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    Date Created:

    Oct 09, 2013

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    Oct 03, 2014
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