# “2019年IOAA理论第5题-CMB烤箱”的版本间的差异

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## 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)

## 中文题目

5.宇宙微波背景烤箱（10 p）

a）星系际空间中的宇航员从宇宙微波背景（CMB）吸收辐射能量的大致速率（以瓦为单位）是多少？ CMB的光谱能量分布可通过温度为$$𝑇_{CMB}= 2.728 K$$的黑体辐射来近似。（5 p）

b）宇航员每秒大约吸收多少个CMB光子？ （3 p）

c）忽略其他能量输入和输出，CMB将宇航员的温度提高$$Δ𝑇= 1 K$$需要多长时间？ （2 p）

## 解答

a)CMB的辐射功率满足斯特藩—玻尔兹曼定律

＄＄P=S\sigma T^4＄＄

R=0.24m

S=4πR^2平方米