PHYS 1202 / PHYS 1203 / PHYS 2311
Physics for the Life Sciences

Sample Answers, Question Sheet 6, 1999

Revision Questions - use these to guide your revision

  1. Conduction, convection and radiation are the three means by which heat can be transferred. In what important way does radiation differ from the other two?
  2. Stefan's Law for the power radiated by an object at temperature T is:

    P = $\displaystyle \sigma$AeT4  .

    Discuss the emissivity e, and explain what is meant by a black body. What is the value of e for a perfect absorber? A perfect reflector?

  3. Explain the term basal metabolic rate, and use it to explain why a resting nude person can become cold, even in a relatively warm room.
  4. Give examples of oscillating/vibrating systems, both mechanical and non-mechanical.
  5. Define the terms period, frequency and amplitude.
  6. What is meant by resonance?

Discussion Questions - for workshops and tutes

  1. Medical thermography (or thermology as it is sometimes called) is the clinical use of the infra-red radiation emitted by the surface of the body. A good description of the technique, with clinical examples, can be found at the Thermascan web site:

    http://www.thermascan.com/home.htm

    Keep in mind that this is a commercial web site, with a product to sell. We are purely interested in the technique, not in evaluating the claimed clinical outcomes.

    One of the claims made is that thermography "...is seen as an attractive means of medical testing because it is absolutely safe, quick, simple for the patient..." Does the claim of absolute safety seem reasonable? Contrast with a medical x ray.

    Thermography is a passive process: it relies on detecting the infra-red radiation emitted by the patient. (See Problem 2: a temperature difference of a couple of degrees C changes the rate of energy emission by a couple of percent.) Because of this, it is diff\icult to imagine how the process could be dangerous, except perhaps that the patient might get cold! A medical x-ray, by contrast, involves firing x rays at the patient. It is known that there is a small risk of contracting cancer from exposure to x rays, but hopefully this risk is small compared to the potential benefits.

  2. A thin-walled stainless steel cup contains water at 89 oC. The outer surface of the cup is highly polished, and there are two pieces of masking tape - one white and one black - stuck to it. Explain why an infrared thermometer, preset to measure the temperature of objects with emissivity of 0.95, records temperatures of 32 oC, 89 oC and 89 oC when pointed at the shiny steel, the white tape and the black tape respectively. Can a black body be white?

    The cup, the black tape, and the white tape all have approximately the same temperature. Clearly, the thermometer does not work properly when it is asked to measure the temperature of the shiny metal surface. The reason it that while the tape - along with many other objects - has emissivity in the region of 0.95, the shiny surface has a much lower emissivity. The rate of energy emitted by radiation depends directly on the emissivity, thus the cup radiates less energy per unit time than a surface at the same temperature, but with higher emissivity. In fact, the cup is radiating the same amount of energy per unit area as an object with high emissivity (about 0.95) at a temperature of 32 oC! Note that  black body simply means an object with emissivity 1: by this definition, the black and white tape qualify as "black bodies".

  3. Under what circumstances can a thermometer in an incubator with a baby be a poor indicator of the temperature of the baby? (Hint: A shiny thermometer can often have a very low emissivity - making it a poor emitter of radiation as in the previous question - but a baby's skin has e $ \simeq$ 1.)

    A shiny thermometer may be a poor emitter/absorber of radiation (viz the shiny cup in the previous question), so heat transfer will have to occur by conduction and convection. The baby's skin, on the other hand, is an excellent emitter/absorber of radiation. If the walls of the incubator are all at the same (room) temperature, there will not be a big problem. The baby will exchange energy with the walls by radiation, but this should not remove too much energy from the baby. The big problem arises if one or more walls of the incubator are cold: this can happen if the incubator is placed near a an uncovered, cold window. In this case, the incubator can cool due to radiation to the cold window, and the baby can cool due to radiation to the cold incubator. The thermometer, however, is not a good radiator and so may not cool in the same way. Other means of recording the baby's body temperature are required: eg a rectal or infrared thermometer.

Problems - these will be marked, and will count towards your final grade in the topic

Due 5:00 PM on Monday 13th September.

  1. The sun has radius 6.96 x 108 m and surface temperature close to 6000 K. If its emissivity is e $ \simeq$ 1, how much energy does the sun radiate each second?

    P = 4.47 x 1026 J/s

    It's interesting to note that this power is about the same as would be radiated by Avogadro's Number of 1 kW bar radiators!

  2. Two regions of skin have different temperatures: T1 = 33.0oC and T2 = 31.6oC. Find the ratio of the rate at which energy is radiated by 1 cm2 of skin in region 1 to the rate at which energy is radiated by 1 cm2 of skin in region 2. That is, find P1/P2.

    P1/P2 = 1.0185, ie P1 is about 2% greater than P2.

    What does this suggest about the accuracy required if a thermograph is to distinguish between the temperatures of these two regions?

    The emitted radiation needs to be measured with accuracy better than 2%.

  3. A copper pipe containing hot water has length 3 m, outer diameter 12 mm, and outer surface temperature 80 oC. If the emissivity of the surface is e = 0.95, and the surroundings are at 20 oC, at what net rate does the pipe lose thermal energy due to radiation?

    P = 49.7 W

  4. A pendulum consists of a mass at the end of a very thin rod. What is the length of the rod if the period of the pendulum is 1.00 s?

    L = 0.24824 m

  5. A clock uses a pendulum built from brass, which has a coefficient of linear expansion $ \alpha$ = 19 x 10-6 (oC)-1. The clock keeps perfect time at 20 oC. (a) At 0 oC, does the clock gain time or lose time? (b) How much time does it gain or lose each hour?

    (a) Pendulum is shorter, so period is shorter: Gains time.    (b) Gains approx 0.7 s each hour

    This problem can be done without knowing the intitial length L0 of the pendulum, by taking the ratio of the periods at the two different temperatures. Students who are comfortable with a bit of algebra should try it this way. Otherwise, use the length calculated in the previous question as the "20 oC" length.
Leon Mitchell
1999-09-06