Problem Statement of Series 5, Year 38
About the Competition Rules How to Write Solutions Results1... square?
3 points
Jindra owns a sheet of paper with a square hole cut out in the middle. The hole has
a side length
2... waterlift
3 points
We fill a hose with water—one end is submerged in a water reservoir, while the other
end is sealed airtight. We then start pulling the hose vertically upward. This water
has a temperature of
Hint: Consider how strong the vacuum will be at the sealed end.
3... they got off on the orbit
5 points
Tomáš boarded a train, sat in one of the carriages, and decided to take a nap.
When he woke up, he found out he was alone in the carriage, and the carriage,
along with him, was orbiting the Earth at an altitude of
Tomáš was excited because he realized he could take advantage of the inhomogeneity
of the Earth's gravitational field to measure the length of the carriage. He took
two
4... minigolf see-saw
8 points
Maybe you have gone minigolfing at a course where one of the holes featured a see-saw
obstacle. We can model the see-saw as a board of mass
5... rise, entropy, rise
9 points
Marek has two identical metal cubes with constant heat capacity
Hint: If you get stuck, remember that entropy will never decrease.
P... Dodo doesn't want to die
9 points
Which isotope is the most dangerous in terms of nuclear power plant accidents? Consider the amount that could be released during an accident, the likelihood of a leakage, the spreading of specific isotopes and their impact on the human body.
E... weh di hell mi deh?
13 points
Try to measure your latitude as accurately as possible without using GPS or any other method that relies on information about your location. You can assume your longitude to be a known quantity.
Instructions for Experimental TasksS... Electrochemistry 5–-transfer of mass and RDE
10 points
- In the Levič equation, physical quantities on the right-hand side appear with non-integer exponents. Verify that both sides of the equation have the same units. – 1 point
- In a beaker intended for a rotating disc electrode, we dissolved
of seventy percent perchloric acid in of pure water and mixed everything thouroughly. Then, on a platinum working electrode with a circular shape and a diameter of , we varied the voltage for the hydrogen formation reaction until we reached the limiting current of . After measuring it, we started spinning the electrode at a frequency of , where the limiting current was . Determine the diffusion coefficient and the thickness of the diffusion layer before spinning. The kinematic viscosity of water is . – 3 points - Find the highest power that a galvanic cell with the following parameters
can provide and determine the corresponding load. For simplicity, consider the Tafel
regime with a Tafel slope of
and a parameter . The ohmic resistance is . The open-circuit voltage is . Neglect the diffusion regime. – 3 points - Derive the Koutecký-Levič equation as presented in the series text. Start from
the derivative of the Levič equation in the case
where
. – 3 points