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4. Series 21. Year - 2. heating of a sphere

In this question we investigate influence of temperature on to moment of inertia of a metal body. Lets have an axe going through the body. How will change the moment of inertia $J$ when the temperature is increased by $ΔT$, if the coefficient of thermal expansion of metal is $α$. If you have problem with a arbitrary shape of body, consider sphere of cylinder.

V Havránkovi se úloha líbila Pavlu Motlochovi.

5. Series 20. Year - P. what type of windows?

One of organizers recently upgraded his windows in his house. They are now double-glazed. The space between two glass tables can be filled by inert gas or vacuum. Suggest a method to distinguish between these two types windows (without destroying windows).

Problém ze života Michaela Komma.

3. Series 20. Year - 4. Albert Einstein's heating

Albert Einstein in his retirement (in contrary to his peers working in the back gardens) still enjoyed solving difficult puzzles. In winter he noticed that water heated directly in fire gets war very slowly and the efficiency is small.

He decided to try other method: Take ideal heat machine and use boiler and air as hot and cold reservoir. Then use the gain work to another ideal heat engine which will get heat from air and transfer it to water. If the temperature of boiler, water and air is $T_{1}$, $T_{2}$ and $T_{3}$, what is efficiency of water heating? Does it conflict with second thermodynamic law?

Úlohu navrhl Matouš Ringel.

5. Series 19. Year - 2. PET at a window

A PET bottle was left at a window in a well heated room. The temperature outside is well bellow zero Celsius. Someone opened the window and forget to close it and temperature in the room is now also well under zero. What is relative change of volume of bottle at a window?

Úlohu vymyslel Jano Lalinský.

5. Series 19. Year - 3. efficiency of power station

Calculate the efficiency of a machine working between two thermal baths of temperatures $T_{1}$ and $T_{2}$, $T_{1}>T_{2}$ which is making biggest possible power. To final equation substitute data from some known power station.

Do not forgot, that Carnot's engine has zero output, because at isothermal process the difference of temperatures between the engine and the bath is infinitesimally small which causes infinitesimally small heat flux causing infinitesimally small output power of the engine.

Úloha z knížky Herbert Callen.

5. Series 19. Year - E. grandma's pancakes

Heat up a pan on the heat source to temperature ideal for pancake preparation (approx 200° C). If you drop a drop of water it will not evaporate immediately and will be running on the pan for up to one minute. Measure the time of life of the drop versus the size of the drop and try to explain.

Úlohu navrhl Jan Lalinský.

4. Series 19. Year - 2. expedition to the planet of the balloons

A big expedition to the planet of the balloons is being prepared. Preliminary data show following physical characteristics: the atmosphere consists of air of fly-weight 10001 lufts per fly and number of molecules in one fly is 10^{1101}, the thickness of atmosphere is 10^{10001} spurgles and by comparing of temperatures it was conducted that 7K on Earth corresponds to 1 luft times square spurgl per square temp.

Calculate temperature at the surface and decide if the astronauts should wear t-shirt or rather fur coat. The solution of IV.1 can help you.

Úloha ze starého ročníku FYKOSu.

4. Series 19. Year - P. balloon-refugee


After a small revolution on planet of balloons one of balloons took refuge on Earth. First he was quarantined and his volume $V$ and temperature $T$ were measured.

However the immigration department decided that the balloon will not be freed until his volume is $V'$ and temperature $T'$. The balloon is not allowed to release or receive any heat or change the number of particles. What is the best way to reach required parameters and be released and live happy ever after on Earth?

Problém Matouš slyšel na přednášce prof. Koteckého a vymyslel řešení.

3. Series 19. Year - 3. delayed bath

Robin managed to get a bath full of hot water of temperature $T_{1}$ and volume $V_{1}$.

Robin's long-term dream was to isothemally compress gas of temperature $T$, volume $V_{0}$ and density $ρ$. And here it was an ideal occasion. As the cooler he used ambient air, which amount and heat capacity is unlimited and whose temperature is $T_{2}$. Calculate what is minimum volume $V$ to which he can compress the gas, if he uses only the warm water in the bath and newly constructed heat-engine.

Robin se nechal inspirovat na přednášce z termodynamiky.

2. Series 19. Year - 4. heat conductivity of metals

Derive the temperature dependence of heat conductivity of metals, if the temperature dependence of electrical conductivity is known.

For free electrons in metal the model of ideal gas can be used, e.g. free electrons are moving without external forces on straight lines (ions are not considered) and sometimes collides with other electrons, when they change the direction and amplitude of velocity.

The heat transferred by crystal lattice is negligible to the heat transferred through free electrons. Each electron has heat capacity $c$, which is temperature independent.

Honza při čtení Ashcrofta.

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