A heat lamp emits infrared radiation whose rms electric field is E rms = 3052 N/
ID: 1465214 • Letter: A
Question
A heat lamp emits infrared radiation whose rms electric field is Erms = 3052 N/C.
(a) What is the average intensity of the radiation?
W/m2
(b) The radiation is focused on a person's leg over a circular area of radius 4.3 cm. What is the average power delivered to the leg?
W
(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 1.9 C°? Assume that there is no other heat transfer into or out of the portion of the leg being heated.
Explanation / Answer
eo =8.85x10^-12 C^2/N.m^2
c =3x10^8 m/s
Iav =(1/2)eoEo^2c= (1/4)eoErms^2c
Iav = (1/4)(8.85x10-12)(3052x3052)(3x108)
Iav = 6182.65 W/m2
(b) R = 4.3 cm
Iav =Pav/A =
Pav = Iav(4pir2) = (6182.65)(4*3.14*0.043*0.043)
Pav = 143.6 W
(c) m = 0.29 kg , Cp =3500 J/kg. · C° , dT = 1.9 · C°
Q = mCpdT
P = Q/t
Pt = mCpdT
t = mCpdT/P = (0.29*3500*1.9)/143.6
t = 13.43 s