2. Temperature and Illumination Alone in your dim, unheated room, you light a single candle rather...

2. Temperature and Illumination

Alone in your dim, unheated room, you light a single candle rather than curse the darkness. Depressed with the situation, you walk directly away from the candle, sighing. The temperature (in degrees Fahrenheit) and illumination (in % of one candle power) decrease as your distance (in feet) from the candle increases. In fact, you have tables showing this information. (tables are in the text).

You are cold when the temperature is below 40◦. You are in the dark when the illumination is at most 50% of one candle power.

(a) TwographsareshowninFigures2.70and2.71.Oneistemperatureasafunctionofdistance and one is illumination as a function of distance. Which is which? Explain.

Figure 2.70 Figure 2.71
(b) What is the average rate at which the temperature is changing when the illumination drops from 75% to 56%?
(c) You can still read your watch when the illumination is about 65%. Can you still read your watch at 3.5 feet? Explain.
(d) Suppose you know that at 6 feet the instantaneous rate of change of the temperature is −4.5◦F/ft and the instantaneous rate of change of illumination is −3% candle power/ft. Estimate the temperature and the illumination at 7 feet.
(e) Are you in the dark before you are cold, or vice versa?

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genius_generous answered 2 years ago

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