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## thermodynamics

### (10 points)6. Series 33. Year - S.

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### (12 points)5. Series 33. Year - E. if Jáchym don't oil, Matěj will oil

Measure the time dependence of the temperature of a liquid in an open mug. Use water first, than oil and finally water with a thin layer of oil. The layer should be as thin as possible but still should cover the whole surface. Measure between $90 \mathrm{\C }$ and $50 \mathrm{\C }$. Be careful to keep all conditions same for all experiments (the same mug, the same initial temperature, keep the thermometer on the same place in the liquid etc.). Describe your experimental equipment, compare cooling in individual cases and discuss the result.

Karel ate a bowl of steamy soup in tropically hot weather.

### (10 points)5. Series 33. Year - S. min and max

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They had to wait a lot for Karel.

### (3 points)4. Series 33. Year - 2. Mach number

Planes at high flight levels are controlled using the Mach number. This unit describes velocity as a multiple of the speed of sound in the given environment. However, the speed of sound changes with height. What is the difference in the speed of a plane, flying at Mach number $0{,}85$, at two different flight levels FL 250 ($7\;600 \mathrm{m}$) and FL 430 ($13\;100 \mathrm{m}$)? At which flight level is the speed higher and by how much (in $\jd {kph}$)? The speed of sound is given by $c =$331{,}57+0{,}607\left \lbrace t \right \rbrace$ \jd {m.s^{-1}}$, where $t$ is temperature in degrees Celsius. Assume a standard atmosphere, where temperature decreases with height from $15 \mathrm{\C }$ by $0,65 \mathrm{\C }$ per $100 \mathrm{m}$ (for heights between $0$ and $11 \mathrm{km}$) till $-56{,}5 \mathrm{\C }$, and then remains constant till $20 \mathrm{km}$ above mean sea level.

Karel was learning Air Traffic Control.

### (10 points)3. Series 33. Year - P. meteor swarm

Is it possible that droplet of rain evaporates earlier than it hits the ground? Think up suitable model of evaporating of rain droplets during their fall and show under what conditions (some of the relevant parameters are initial radius, behaviour of outdoor temperature in relation to height above sea level) the droplet can evaporate completely. You can assume that the droplet arises suddenly in particular height $h_0$ with initial radius $r_0$ and in first approximation it falls through dry atmosphere. And when is it possible that the droplet freezes?

Mirek waited for rain.

### (3 points)4. Series 32. Year - 1. cube with the air

Consider a hollow cube with edge of $a = 20 \mathrm{cm}$ filled with air. Air as well as the enviroment has a temperature of $t_0 = 20 \mathrm{\C }$. We will cool down the air inside the cube to the temperature of $t_1 = 5 \mathrm{\C }$. Find the force acting on each of the cube's side. The cube has got a fixed volume. The pressure outside of the cube equals $p_0 = 101{,}3 \mathrm{kPa}$.

Danka was irritated by the shower curtain.

### (3 points)3. Series 32. Year - 2. efficient coffee

It is 2 am and Jáchym is going to make a coffee. He places a kettle with the heat capacity of $C_k$ on a hot plate, which is made of a cast-iron cylinder of a radius $r$ and of height $h$. The kettle contains water with a volume of $V$ with an initial temperature of $T\_v$. The rest of the system has got an initial temperature of $T\_s$. What is the overall efficiency (ratio of energy absorbed by water vs energy input) of water heating from its initial temperature $T = 100 \mathrm{\C }$ $(T\_s, T\_v < T).$ Assume, that the heat transfer is very fast and therefore there is no heat loss. You can estimate the unknown values or find them in physics tables.

Jáchym run out of energy drink

### (6 points)3. Series 32. Year - 3. heat in the Dyson sphere

What would be the diameter of a Dyson sphere that would surround a star with the luminosity of the Sun, so the temperature on the outer surface of the sphere is $t= 25 \mathrm{\C }$?. Don't consider the presence of the atmosphere in the Dyson sphere. A Dyson sphere should be a relatively thin concave structure of spherical shape surrounding the star.

Karl likes Dyson spheres.

### (3 points)2. Series 32. Year - 2. Finnish sauna

Imagine that Dan has a sauna with dimensions $2,5 \mathrm{m}$ x $3 \mathrm{m}$ x $4 \mathrm{m}$ with a relative humidity of $20 \mathrm{\%}$ and temperature of $90 \mathrm{\C }$. How much water would have to evaporate, so the relative humidity inside the sauna is $35 \mathrm{\%}$? The water evaporates inside the sauna without changing the overall temperature.

### (10 points)2. Series 32. Year - P.

Create an accurate weather forecast for address V Holešovičkách 2, Prague 8, for Wednesday 14th of November from 12:00 to 15:00. How will the weather change throughout the whole day? You are allowed to use previous data about the weather in this area (remember you are only permitted to use data until 10th of November). It is necessary to justify your weather prediction, write down references and ideally to use as many data and resources as possible.

Karl listened to radio on a motorway