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## statistical physics

### (10 points)2. Series 33. Year - S.

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

### (10 points)6. Series 32. Year - P. problem of high-way safety

* *

- How many cars going on the road per unit of time are needed to keep the road dry in case of raining?
- How many cars going on the road per unit of time are needed to keep the road dry (i.e. there is neither snow nor ice on the road) in case of snowing? The temperature of the snow is comparable to the surroundings (i.g. several degrees bellow zero).

Assume constant normal rate of precipitacion.

Karel drove on the high-way

### (6 points)3. Series 31. Year - 3. IDKFA

You fired at Imp from your plasma gun which shoots a cluster of particles with uniform velocity distribution in interval $\langle v_0, \; v_0+\delta v\rangle$ (all of the particles are moving in one line, there is no transverse velocity). The total kinetic energy of the cluster is $E_0$. The barrel rifle has a cross cestion of $S$ and the pulse takes an infinitely short time. How far does Imp need to stand to be safe. Assume that his skin is able to cool the heat flow of $q$.

### (3 points)0. Series 31. Year - 2.

### (9 points)4. Series 30. Year - P. statistician's daily bread

We've all been there, you spread some honey or some preserve on a slice of bread, take a bite, and suddenly, the spread drips through a hole and lands right on your hand. Determine how does the probability that there is a hole straight through a slice of bread depend on its thickness. The model of how does the dough rise is left up to you. (For example, evenly distributed bubbles with an exponential distribution of radii is a good model).

Michal stained his clothes.

### (2 points)5. Series 29. Year - 2. multiparticular

Let's have a container that is split by imaginary plane into two disjunct parts A and B, identical in size. There are $nparticles$ in the container and each of them has a probability of 50 % to be in part A and probability 50 % to be in part B. Figure out the probabilities of the part A containing $n_{A}=0.6n$ or $n_{A}=1+n⁄2$ particles respectively.. Solve it for $n=10$ and $n=N_{A}$, where $N_{A}≈6\cdot 10^{23}$ is Avogadro's constant.

### (2 points)6. Series 26. Year - 1. disgusting water

Many years ago you drank 2 dcl of water. Imagine that since then all the water on the Earth has mixed. If you drink 2 dcl of water today, how many molecules from the original water you drank does it contain?

Karel is afraid of cholera.

### (2 points)1. Series 26. Year - 2. show us your insides

Estimate the number of electrons in an adult human body.

Karel was playing his insides.

### 6. Series 19. Year - S. last question

- Describe qualitatively how the behavior of heat capacity of Ising model with zero external magnetic fields around critical temperature.
- Using similar approach, as we calculated behavior of magnetization $m$ in vicinity of critical point, calculate behavior of susceptibility $\chi (lim_{B\rightarrow0}\partial m⁄\partial$ B)$ and dependence of magnetization on magnetic field around critical temperature.
- Show, that the model of lattice gas gives condensation and find critical temperature.
- Investigate the model of binary alloy.

Zadal autor seriálu Matouš Ringel.

### 5. Series 19. Year - S. fermions and bosons

- Find a density of states $g(E)$ for free electrons and using this equation find relation between number of electrons and Fermi energy at zero temperature. Find out, what must be the Fermi energy dependence on temperature (for low temperatures) for constant number of electrons. Estimate number of excited electrons at room temperature

**Hint:** Take inspiration from last parts of our series and the problems accompanying them.

- Calculate dependence of μ versus temperature at low temperatures and constant number of particles in the system o identical bosons. Find the temperature dependence of number of excited bosons at low temperatures.

Zadal autor seriálu Matouš Ringel.