Physics of Energy & the Environment- PHYS 161

Lecture 12

Reading: Chapter 24, pages 550-562.

Reminder-- Homework (assigned Tuesday, 2-November): Chapter 8, problems 2, 3, 6, 7, 9, 27, 36, 38. Due Thursday, November 11.

Heat and Temperature

What happens when a piece of hot metal is dropped in room temperature water. Over time the metal will cool and the water will heat up. Eventually the two objects will have the same temperature. They are then said to be in thermal equilibrium with one another.

During the intervening time the hot metal is transfering energy to the water. How can we tell?

The water can do more work than it could before. The water might boil, for example. A piston could be placed over the water in a sealed container, and the piston would lift, much like the lid rattling on a pot of boiling water. The piston would gain gravitation potential energy in lifting, so the heated water did work on it. The original energy came from the hot piece of metal.

So energy is transferred from the hot metal, eventually, to the piston. Evidently "heat" involves an energy transfer. And a temperature difference is necessary for that energy transfer to take place.

Consider a simple model comprising hot gas molecules in a cool box.If we built our box with transparent sides and could somehow see the molecules inside, what would they be doing? What if we marked just one molecule so that we could see it, and restrained its motion to two dimensions?

Here are some questions to ask yourself when watching this movie:

An aside on absolute zero

You will remember that the temperatures given above for black bodies were listed in "Kelvins." What is a Kelvin? Why do we use it?

It turns out that there is a temperature--absolute zero-- where particles in a system have no kinetic energy (they don't move). The temperature of such a system is 0 Kelvins. So Kelvins are units of temperature which reference absolute zero.

We can estimate absolute zero with a simple demonstration, predicated on the proportional relationship between temperature and pressure for an ideal gas at constant volume.

Adiabatic Compression

We spoke of transfering heat energy to water from a piece of hot metal. Typically the water, in turn, loses its newly-gained thermal energy to its surroundings. The whole process takes time.

What if we do work on a gas and don't give it time to lose heat energy to its surroundings. What happens to the gas?

Interactive Lecture Demonstration, Part B:

We can simulate what happens to the gas molecules during adiabatic (no heat transfer) compression by using the following QuickTime movie:

When we do work on the system (W), we increase its internal energy (DU, following the notation in our textbook), as evinced by an increase in temperature. We can state this finding as a simple equation:

This says that doing work on a system changes its internal energy by an amount equal to the work. (what happens if work is done by the system?)

We can do a demo that shows this increase in internal energy very dramatically:

First Law of Thermodynamics

Now what if I very slowly pushed down on the plunger? Would the paper ignite? Why or why not?

Pushing down slowly gives the system (gas in the tube) time to cool down, via heat energy transfer to its surroundings. So, evidently, transfering heat energy (-DQ) to its surroundings decreases internal energy.

{If we define DQ to be heat transfered to the system, then -DQ is heat energy transferred from the system.} We can summarize this as follows:

This is just a statement of energy conservation in disguise. In fact, this is the most general statement of energy conservation one can make. The (internal) energy of a closed system changes by transferring heat energy in (DQ is positive) or out of it and by doing work on it (W is positive) or having it do work on its surroundings.

Other ways to change internal energy

So how do we tell what the internal energy of a system is? It seems we should take its temperature, but there are other ways to change internal energy without changing temperature.

Sunlight absorbed by ocean water can raise the water's temperature. Or it can cause the liquid water to turn into water vapor, even though the water is NOT boiling. This is how energy from the sun drives the hydrological cycle:

In the Pacific Northwest and elsewhere humankind exploits the hydrological cycle-- a mechanism whereby fresh water is transported to and from oceans; into and out of lakes, streams and glaciers; and back and forth from underground reservoirs-- to provide electrical energy from a hydroelectric plant.
We also rely on the hydrological cycle to:
  • Transfer energy from the sun falling on the oceans to continents.
  • Distribute more equally water resources across land masses.
  • Increase erosion of rocks and soils covering the continents.
  • Regulate atmospheric temperature (see point 1).

Thanks, Greg!

The latent heat of evaporation describes the amount of heat energy transfer necessary to turn a given amount of liquid water into vapor form. This energy ultimately derives from the sun. The conversion of the sun's energy to evaporate ocean water is one of the primary mechanisms driving the hydrological cycle.

So hydroelectricity is just another form of "solar energy!"

Mechanisms for Heat Energy Transfer

Heat energy can be transfered by three different mechanisms:

Radiation of heat energy from the sun is responsible for life on Earth.

An example-- Energy conservation in the home

    To better understand the three mechanisms for heat energy transfer, imagine you were charged with doing things to lower the heating bill (weatherize) an ancient cathedral in Bath, England.

  1. The first thing you should do is repair all those fancy windows and doors. They are a source for drafts (not the game played in pubs), where warm air leaks to the outside and is replaced by cold air from outside. This is heat energy by convection, because warm air is moving, taking heat energy with it. Studies show that cutting down air leakage is the most cost-effective form of weatherization.
  2. The next thing to consider is insulating the ceilings, walls and floors of the cathedral. Insulation cuts down on heat energy transfer out of the building via conduction. As warm air typically accumulates near the ceiling (why is that?), a greater difference in temperature exists between the ceiling and outdoors than elsewhere in the building. That is the place to start adding insulation.
  3. After you have caulked (cut drafts) and insulated ye ole cathedral, its time to think of extreme measures. For example, you might want to paint the outside of the cathedral black so that it better absorbs heat energy from the sun. Why is this extreme? Well, it really is the least cost-effective thing you can do. Heat loss or gain by radiation is usually a small factor affecting a building heat budget. Besides, whether this helps or not really depends on the temperature outdoors. During summer you may end up overheating the cathedral. And then where would they sing evensong?

To get a perspective on how the energy used to heat buildings compares to other forms of energy use in the US, let's look at table 24.3 from your textbook:

Use
Percent of US Fuel Consumption
Second-Law Efficiency (%)
Space heat
      18
      6
Process steam
      17
      25
Auto transport
      13
      10
Truck transport
      5
      10
Water heat
      4
      3
Air conditioning
      2.5
      5
Refrigeration
      2
      4

Evidently space heating represents a substantial part of the US energy budget!

All that aside, conservation of a building's thermal energy can be thought of as another energy source. Because a weatherized building uses less energy for heating, that saved energy can be used elsewhere. Conservation of thermal and other forms of energy has an added benefit. Compared to the second-law efficiencies of various energy conversion processes (we'll get to that next lecture), energy conservation is 100% efficient!

For more information about heat transfer mechanisms and weatherizing a home, see Prof. Bothun's page on insulation in the home.

We can do a simple calculation to estimate the yearly energy savings when insulating a house. Insulating a house involves cutting heat energy loss by conduction. The rate at which heat flows through a system boundary (Q) is given by:

where k is the thermal conductivity, A is the area of the boundary (say the wall of a house), DT is the temperature difference across the boundary, and t is time.

We can restate this rule in more common units of thermal resistance, R, as:

The "R-value" of insulation is typically written on home insulating materials and, in the US, assumes units of square feet and temperature differences in degrees Farenheidt. Its US units are {hr ft2 oF / BTU} (note the hour).

For a home with a given R-value for walls, ceilings and floor, and a fixed area for heat energy transfer, a greater difference in temperature (DT) results in a greater heat flow rate. The average daily difference between the temperature outdoors and an assumed indoors temperature of 65 oF is called a degree-day.

Degree-days are compiled for various locations around the US and abroad. For example, the degree-days for Eugene are approximately 4,200.

If the Eugene heating season is 150 days long, what is the average daily outdoor temperature?

So degree-days are a convenient way of stating both temperature difference and time. To calculate heat loss by conduction using degree-days, we write:

(The hour/day conversion converts degree-days to degree-hours, so as to cancel with the hours in the units of R.)

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