Chapter 24, Problem 60 A heat lamp emits infrared radiation whose rms electric f

Question

Chapter 24, Problem 60

A heat lamp emits infrared radiation whose rms electric field is Erms = 3600 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 5.0 cm. What is the average power delivered to the leg? (c) The portion of the leg being radiated has a mass of 0.31 kg and a specific heat capacity of 3500 J/(kg·C°). How long does it take to raise its temperature by 2.1 C°? Assume that there is no other heat transfer into or out of the portion of the leg being heated.

Explanation / Answer

given data: Erms = 3600N/c c = 3.0*108m/s 0 =8.85*10-12C2/Nm2 radius r = 5.0*10-2m so contact area A = r2 = 78.55*10^-4 m^2 a) the average intensity of radiation is Iav =c0Erms2 Iav = 3*10^8*8.85*10^-12*(3600)^2        = 34408.8 W/m^2 (or) Iav = 3.44*10^4 W/m^2 b) the average power is      Pav =Iav*A     Pav = 3.44*10^4 W/m^2*78.55*10^-4 m^2         = 270.21 W c) mass m = 0.31 kg and specific heatcapacity C = 3500 J/(kg x C).    change in temperature is T =2.10c time required is      t = mCT / Pav     t = 0.31*3500*2.1 /270.21       = 8.43 s     t = 0.31*3500*2.1 /270.21       = 8.43 s

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