2019年IOAA理论第5题-CMB烤箱

英文题目

5. Cosmic Microwave Background Oven (10 p)

Since the human body is made mostly of water, it is very efficient at absorbing microwave photons.

Assume that an astronaut’s body is a perfect spherical absorber with mass of $$𝑚 = 60 kg$$, and its average density and heat capacity are the same as for pure water, i.e. $$𝜌 = 1000 kg m^−3$$ and $$𝐶 = 4200 J kg^−1 K^−1$$.

a) What is the approximate rate, in watts, at which an astronaut in intergalactic space would absorb radiative energy from the Cosmic Microwave Background (CMB)? The spectral energy distribution of CMB can be approximated by blackbody radiation of temperature $$𝑇_CMB = 2.728 K$$. (5 p)

b) Approximately how many CMB photons per second would the astronaut absorb? (3 p)

c) Ignoring other energy inputs and outputs, how long would it take for the CMB to raise the astronaut’s temperature by $$Δ𝑇 = 1 K$$? (2 p)