Thermo warm-up

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If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equations---then so much the worse for Maxwell's equations. If it is found to be contradicted by observation---well these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation.
Sir Arthur Stanley Eddington

Problem 1: the cold of space

When designing a suit for open space, what should engineers be more careful of: heating or heat extraction?

Problem 2: calculating photons

Estimate a number of photons in a gas oven at room temperature and at maximum heat.

Problem 3: equilibrium

Estimate the temperature at the surface of the Sun, assuming that the Earth with mean temperature at its surface $15\,C^\circ$ is in thermal equilibrium with the Sun.

Problem 4: entropy of gravity

What is the difference between entropy of gravitational degrees of freedom and ordinary entropy (e.g., entropy of ideal gas)?

Problem 5: the Sun as the source of low entropy

One of the most used classifications divide physical systems into open and isolated. The entropy in an isolated system can only increase, eventually reaching the maximum at thermal equilibrium. In contrast, in open systems the entropy can decrease due to external interactions, for example, through absorption of a component with low entropy. Explain why the Sun is a source of low entropy for the Earth.

Problem 6: infrared vs ultraviolet photons

Estimate how many infrared photons Earth radiates per one ultraviolet photon it absorbs from the Sub.

Problem 7: entropy gain of the Universe per person

A human during his lifetime increases the entropy of the Universe by converting chemical energy contained in the food to heat. Estimate the corresponding entropy gain.

Problem 8: Earth's entropy production

Estimate the contribution of Earth during its existence to the entropy production.

Problem 9: Sun's entropy production

Show that the Sun has contributed the entropy increase of about $10^{40} J/K$