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1. Determine the energy gain of the following reactions and the kinetic energy of their products

\[\begin{align*} {}^{2}\mathrm {D} + {}^{3}\mathrm {T} &\rightarrow {}^{4}\mathrm {He} + \mathrm {n}  ,\\ {}^{2}\mathrm {D} + {}^{2}\mathrm {D} &\rightarrow {}^{3}\mathrm {T} + \mathrm {p}  ,\\ {}^{2}\mathrm {D} + {}^{2}\mathrm {D} &\rightarrow {}^{3}\mathrm {He} + \mathrm {n}  ,\\ {}^{3}\mathrm {T} + {}^{3}\mathrm {T} &\rightarrow {}^{4}\mathrm {He} + 2\mathrm {n}  ,\\ {}^{3}\mathrm {He} + {}^{3}\mathrm {He} &\rightarrow {}^{4}\mathrm {He} + 2\mathrm {p}  ,\\ {}^{3}\mathrm {T} + {}^{3}\mathrm {He} &\rightarrow {}^{4}\mathrm {He} + \mathrm {n} + \mathrm {p}  ,\\ {}^{3}\mathrm {T} + {}^{3}\mathrm {He} &\rightarrow {}^{4}\mathrm {He} + {}^{2}\mathrm {D}  ,\\ \mathrm {p} + {}^{11}\mathrm {B} &\rightarrow 3\;{}^{4}\mathrm {He}  ,\\ {}^{2}\mathrm {D} + {}^{3}\mathrm {He} &\rightarrow {}^{4}\mathrm {He} + \mathrm {p} . \end {align*}\]

1. By using the graph of fusion reaction rate (sometimes called volume rate) as a function of temperature in the Serial study text, derive the Lawson criterion for the inertial-confinement-fusion time for a temperature of your choosing, while considering the following reactions:

1. deuterium - deuterium,
2. proton - boron,
3. deuterium - helium-3.

Determine the product of the size of a fuel pellet, and the density of a compressed fuel for each case. Are there any advantages of these reactions compared to the traditional DT fusion?

1. What form would the Lawson criterion take for the non-Maxwellian velocity distribution, considering the case with the following kinetic energy of a particle

1. $E\_k = k\_B T^\alpha $,
2. $E\_k = a T^3 + b T^2 + c T$.

Could such a fusion be even possible? If so, what (the fuel) should drive the fusion reaction, what is the ideal size of the fuel pellet and what density should it be compressed to?

Lukáš wanted to cook himself a dinner. He put a pot onto a stove, but forgot to fill it with water (or anything else). The teperature of the pot and the air inside stabilized at $100 \mathrm{\C }$ (do not ask, how he managed that without water). Lukáš realized his mistake and removed the pot from the stove. When the pot had cooled down to the room temperature, however, he was unable to remove its lid with the area $S$ and mass $m$. Calculate the force with which the lid resisted being removed if Lukáš put the lit on the pot

1. just before removing it from the stove and,
2. before the start of dinner preparation.

Assume the air to be an ideal gas.

The ants have a peculiar way of keeping the anthill warm – they crawl out, let the sunlight heat them up, and then crawl back in, where the heat is transferred to the anthill. The anthill can be approximated as a cone of height $H=0{,}8 \mathrm{m}$ with base radius of $R_0=1,5 \mathrm{m}$. The walls are made of cellulose with heat conductivity $\lambda = 0{,}039 \mathrm{W\cdot m^{-1}\cdot K^{-1}}$ and are $2 \mathrm{cm}$ thick.

Assume that the entire heat exchange between the anthill and its surroundings (which have temperature $T\_o = 10 \mathrm{\C }$) is only mediated by the ants and by the conduction of heat through the walls, i.e. neglect the heat exchange with the ground. An ant weighs $m =5 \mathrm{mg}$ and has a specific heat capacity of approximately $4~000 J.kg^{-1}.K^{-1}$. How many ants, heated up to $T\_m = 37 \mathrm{\C }$, have to enter the anthill every second in order to keep the inner volume of the anthill at constant temperature of $T\_M = 20 \mathrm{\C }$?

While baking a gingerbread, baking soda, or more rigidly sodium bicarbonate ($\ce {NaHCO3}$), has to be added into the batter. Let's assume, that at high temperatures sodium bicarbonate decomposes as follows \[\begin{equation*} \ce {2 NaHCO3 \rightarrow Na2CO3 + H2O + CO2} , \end {equation*}\] that is, into sodium carbonate, carbon dioxide and water. How much will the volume of the gingerbread increase as a consequence of creation of water steam and carbon dioxide bubbles in the batter after adding $10 \mathrm{g}$ of sodium bicarbonate? Assume that the water steam and carbon dioxide behave as ideal gases and that the batter solidifies around the bubbles at temperature $200 \mathrm{\C }$ and pressure $1~013 hPa$.

You have probably heard at school about the thermal motion of molecules such as diffusion or Brownian motion. Measure the time dependance of the size of a color spot in water and calculate the diffusion constant. Make measurements for several different temperatures and plot the temperature dependance of the diffusion constant in a graph. How could you arrange the experiment so that the temperature would stay constant during the measurement?

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?

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

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?

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

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.