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

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 = $$\sigma$$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.
   
   
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?
   
   
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.)
   
   

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?
   
   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 = 33.0^oC and T₂ = 31.6^oC. 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.
   
   What does this suggest about the accuracy required if a thermograph is to distinguish between the temperatures of these two regions?
   
   
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?
   
   
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?
   
   
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?
   
   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.