A heat lamp emits infrared radiation whose rms electric field is Erms = 2996 N/C
ID: 1997322 • Letter: A
Question
A heat lamp emits infrared radiation whose rms electric field is Erms = 2996 N/C.
(a) What is the average intensity of the radiation?
(b) The radiation is focused on a person's leg over a circular area of radius 3.7 cm. What is the average power delivered to the leg?
(c) The portion of the leg being radiated has a mass of 0.29 kg and a specific heat capacity of 3500 J/(kg · C°). How long does it take to raise its temperature by 2.3 C°? Assume that there is no other heat transfer into or out of the portion of the leg being heated.
Explanation / Answer
a) For simple plane wave propagation you can derive the time averaged magnitude of this vector as
|S| = (1/2) * vacuum permittivity * c * E02 = vacuum permittivity * c * Erms2
|S| = 8.85 * 10-12 * 3 * 108 * (2996)2
= 2.38 * 104 W/m2
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b) P = |S| A = |S| * pi * R2
= 2.38 * 104 * pi * (3.7 * 10-2 m)2
= 102.49 W
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c) delta Q/ delta t = P
m C deltaT/delta t = P
delta t = m * C * delta T / P
= 0.29 kg * 3500 * 2.3 °C / 102.49
= 22.78 s