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## molecular physics

### (2 points)5. Series 26. Year - 2. molecules

Imagine evaporating a body of liquid with surface area $S$. Assume that during this process all the liquid molecules are separated and tLat each molecule can be considered a small particle with a definite surface area. Obviously, the total surface area of all these molecules is much greater than the surface area of the original body. Given that the latent heat of vaporization of water is $L=2.1\cdot 10^{6}J\cdot \;\mathrm{kg}^{-1}$ and that its surface tension is $α=7.2\cdot 10^{-2}N\cdot \;\mathrm{m}^{-1}$, estimate the size of water molecules.

Dominika was thinking about molecules.

### (8 points)5. Series 26. Year - E. evaporate!

Design an experiment to measure the dependence of the speed of evaporation on the surface area of the evaporating liquid. You should use at least five different containers to do the measurment. What other factors can influence the speed of evaporation? Note that this experiment should run for several days so plan accordingly.

Kiki was too lazy to go get the rag.

### (6 points)5. Series 26. Year - S. series

- Go to this site http://fykos.cz/rocnik26/4-compass.dat and download data gathered with a Langmuir probe from the tokamak COMPASS. Draw the volt-ampere characteristic and estimate the value of the floating potential.

- Given the surface area of the probe ($A=6\;\mathrm{mm}^{2})$ and the composition of the plasma (deuterium), analyze the volt-ampere characteristic and determine the value of electron temperature and density.

- Write a short ode describing the invention of the Langmuir probe.

Robin.

### (6 points)4. Series 26. Year - S. More tokamaks

- Using the expression for the frequency of impacts from the last part of this series, derive a formula for the diffusion coefficient of classical diffusion and calculate its value for a typical plasma in a tokamak.

- Derive a formula for the dependence of the fraction of captured particles on the ratio of the main and small plasma radius $r⁄R_{0}$.

komm

### (6 points)3. Series 26. Year - S. tokamak

- Calculate the specific resistance of hydrogen plasma at temperature 1 keV. Compare your result with the resistance of common conductors.

- Calculate the current necessary to create a sufficiently strong poloidal magnetic field in a tokamak with a major radius of 0.5 m. The toroidal field is created using a toroidal coil with 20 windings per meter. The current inside this coil is 40 kA. The magnitude of the poloidal field should be approximately 1/10 of the magnitude of the toroidal field.

- Create a physical model of the field lines of the force field inside the tokamak, take a photo of it, and send it to us.

### (6 points)2. Series 26. Year - S. drifting

- What kind of drifts can we observe in a linear trap? Assume that the axis of the trap is horizontal. Will the drift caused by the gravitational force have a significant effect on the motion of a particle?

- Derive a formula for the loss cone and draw an original picture illustrating the behavior of a particle in a linear trap.

- Derive a formula for the drift caused by an electric field that is perpendicular to a magnetic field and that has a constant gradient parallel with the electric field. Discuss the the dependence of the particle trajectories on the magnitude of this gradient.

### (6 points)1. Series 26. Year - S. series

- Find out typical properties of a plasma present is the solar wind, in the center of a tokamak and in a low-pressure discharge and calculate the corresponding value of $λ_{D}$.

- Derive an expression for the Debye length of plasma that consists of electrons at temperature $T_{e}$ and ions at temperature $T_{i}$. Do not assume that the ions are static.

- Calculate the electrostatic potential of two infinite parallel conducting planes that are separated by a distance $d$. The potential on these planes is kept $φ=0$ and the space in between these planes is filled with a gas of particles with charge $q$ and concentration $n$.

Robin

### 3. Series 22. Year - 3. save helium

They have a new attraction in „Dolni Dvur“: Helium filled soap bubble, which are just levitating in the air. What is heavier? Helium in bubble or its wall?

Z maďarské přípravy na FO od Dalimila vybral Aleš.