A heat lamp emits infrared radiation whose rms electric field is Erms = 2700 N/C

Question

A heat lamp emits infrared radiation whose rms electric field is Erms = 2700 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 4.1 cm. What is the average power delivered to the leg? (c) The portion of the leg being irradiated 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 2.9 C°? Assume that there is no other heat transfer into or out of the portion of the leg being heated.

Explanation / Answer

Part A

Avg Intensity is given by:

Iavg = 0.5*e0*c*E0^2

E0 = Erms*sqrt 2

Iavg = 0.5*e0*c*Erms^2*2 = e0*c*Erms^2

Using given values:

Iavg = 8.85*10^-12*3*10^8*2700^2

Iavg = 19354.95 W/m^2

Part B

Pavg = Iavg*A

Pavg = Iavg*pi*R^2

Using given values:

Pavg = 19354.95*pi*0.041^2

Pavg = 102.21 W

Part C

energy require to raise the temperature is given by:

Q = m*C*dT

Q = 0.29*3500*2.9 = 2943.5 J

Now we know that

Pavg = Q/t

t = Q/Pavg

t = 2943.5/102.21

t = 28.8 sec

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