Problem Statement of Series 4, Year 38
About the Competition Rules How to Write Solutions Results1... slow connection
3 points
Remote access is often used while observing with telescopes at the La Silla
observatory in Chile. When measuring the data transfer speed, we usually get
a time of
2... boring Earth
3 points
The long forgotten gods of old became very bored while observing Earth. They therefore decided to transform the spherical Earth into a cylinder. The cylinder's axis of rotation passes through the center of its base and is perpendicular to it. What will be the ratio of the day length on the new Earth to the original day length? While they are gods, they are not magicians. Thus, the mass, density, and angular momentum of the cylinder remain the same as those of the original Earth. The height of the cylinder equals the diameter of the original Earth.
3... a sphere in a shadow
5 points
A small sphere is positioned at the furthest possible distance from Earth such
that that it remains completely within the planet's shadow. At what temperature
will the sphere reach equilibrium, assuming Earth behaves as a black body with
a homogeneous temperature of
4... examination time
7 points
Jarda is preparing for his special relativity exam in his vacation house on one
of Jupiter's moons. He was not keeping track of time and found out his exam
begins in two hours (his time is synced with Earth). He got into his extremely
fast rocket and set out for Earth. At the time of takeoff, the distance between
his rocket and Earth equaled
5... smoker at a tram stop
10 points
Jarda is standing at a tram stop, waiting for the tram. However, it still
hasn't arrived, so he decides to walk at a speed
P... sieves
10 points
Propose as many methods as possible for separating substances from a mixture and provide a detailed explanation of the physical principle and experimental procedure for at least three of them. Each one of the three methods described in detail should be based on a different physical or chemical property of the substances.
E... antidune
12 points
Find all-purpose flour and poppy seeds in the kitchen. Verify whether their angle of repose depends on the height of the pile formed by pouring. Additionally, measure the dependence of the angle of repose on the mass concentration of the mixture of plain flour and poppy seeds.
Instructions for Experimental TasksS... Electrochemistry 4 – capacitance and impedance spectroscopy
10 points
- The geometric surface area of our platinum electrode
is
. However, its surface is very rough, so the active surface area may be higher. In an experiment, we measured the capacitance of the whole electrode to be . If we estimate the distance of adsorbed ions in the solution from the platinum surface to be , how many times larger is the active surface area compared to the geometric area? The experiment takes place in water with . – 2 points - Draw the impedance spectrum in a Nyquist plot for a resistor
, a capacitor with capacitance , and CPE with parameters and for the frequencies ranging from to . – 2 points - Determine all the parameters of a Randles circuit from the provided spectrum.
The data points are distributed logarithmically over the frequency range
from
to , with 5 data points per one frequency decade. – 3 points - Impedance spectra of a simple reaction, described by a Randles circuit, were measured at
a DC current
given in the table. From curve fitting the spectra, the ohmic resistance was found to be for all measured values. The charge transfer resistance values are listed in the table below. Assume the measurements were conducted in the Tafel regime. Determine the parameter in the exponential form of the Tafel equation derived in the third episode of the series. – 3 pointsValues of the current and the resistance. measuring 1 0,13 208 2 0,24 99 3 0,57 45 4 1,11 22 5 2,04 14