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## thermodynamics

### (7 points)2. Series 34. Year - 4. lifting ice using heat

A man stores small ice blocks in a well $h = 4,2 \mathrm{m}$ deep. To lift the ice up, he uses a heat engine between ice and the surrounding air with efficiency $\eta =12\%$ of the respective Carnot engine. The temperature of available air is $T\_{air}=24 \mathrm{\C }$. How cold must the ice be at the beggining in order to retrieve it with a final temperature $T_{max}=-9 \mathrm{\C }$? How is it possible even when we heat the ice up in the process?

### (9 points)2. Series 34. Year - P. costly ice hockey

Estimate how much the complete glaciation of an ice hockey rink costs.

### (10 points)1. Series 34. Year - P. Will we survive in vacuum?

Different movies create different conceptions of what and how fast happens when an astronaut's space suit suddenly gets torn. Some of them are even contradictory. Explain what is most likely to happen, if a healthy person finds himself unprotected in a vacuum. What phenomenon is most likely to cause death first?

Kuba planned to travel the world.

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

*We are sorry. This type of task is not translated to English.*

### (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

*We are sorry. This type of task is not translated to English.*

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