Question

3. [10pts] Since we humans are largely made of water, our bodies are efficient at absorbing cosmic microwave photons. Assume that you absorb all incident CMB photons. Heat ca- - 2- pacity of water is C = 4200 J kg-1 K-1. You may assume you weigh 100 kg and span a spherical volume of 1 m3 for simplicity. Clearly explain your line of logic. (a) Estimate the average number of CMB photons in a 1 m3 volume today. (b) Estimate at what rate your body temperature would change as a result of absorbing CMB photon energies. Should you be worried about overheating?

Answer 1

ane luauency range = 300 MHz - 300GH owane - 10-3 mm wavelength = Im - lmm = lm Average wavelength = 0. 5m z +10m = 20.5 = Energy of I photon wc [a wavelength Energy that can be ales orled by 100kg of water 4200 x 100 per K 400000 J at : No. of photous that is present in a im3 volume = bador's 420000 w, 42000 oxo. rs 6.63x10-34 x 3 x 108 1x1030 Photons. x in

by rate at which the temperative of body changes can re given by the expression of E heat energy absorbed in th E = mcao of waten = m = mass of where " leody. AT c = Specific heat of water 10 = change in temperature Rate of change of temperative = 40 total energy allsorbed by the body - nne [n= no. of photons 1 = 2 = frequency of wave Energy is quantised in mits of wy and energy carried by a photous = nur. nny 100*4200 x 40 24 AT - 1x 1030 x 6.63x10 39 x 3x108 0.5mm X 24X60X60 X 100 X 4200 0.039 K/ur :: Rate of change of temperature =