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Determine the dependency of the temperature of the solidification of the aqueous solution of sucrose at atmospheric pressure.

Into a container of volume $V=1\;\mathrm{m}$ in which there is a very low pressure (basically a prefect vacuum) we place $V_{0}=1l$ of water at room temperature $t_{0}$. What will be the final state in which the container and the water in it shall find itself in? For the purposes of the calculation assume that the container is prefectly thermally isolated from its surroundings and and has a negligible heat capacity.

Consider a tyre of a cylindrical shape and of a radius $R$ s an inner radius $rwidthd$ filled up to a pressure of $p$. We push down on the tyre with a force $F$. With this encumbrance the shape of the tyre changes from a cylinder to a cylindrical segment with the same inner and outer radius. Assume that the temperature of the tyre will not change. Determine the contact area of the tyre and road.

Consider a cylindrical container which fills the volume of $V=1l$. The container is closed with an airtight moving piston which has a non-negible mass $M$. Furthermore we know that the container is divided by horizontal partitions into $n$ sections and in the $i-thsection$ (it is numbered from the top ascendingly) there are 2^{$i}a$ particles, where $ais$ an undefined constant.The partitions are not fixed with regards to the container but at the same time they prevent the sections in which the ideal gas can be found from exchanging heat or particles. The whole system is at equilibrium. Then we make the mass of the piston twice as large and wait for equilibrium to arise again. How will the volume of the gas in the container change? Do not consider atmospheric pressure.

Test tubes of volumes 3 ml and 5 ml are connected by a short thin tube in which we can find a porous thermally non-conductive barrier that allows an equilbirum in pressures to be achieved within the system. Both test tubes in the beginning are filled with oxygen at a pressure of 101,25 kPa and a temperature of 20 ° C. We submerge the first test tube (3 ml) into a container which has a system of water and ice in equilbrium inside it and the other one (5 ml) into a container with steam. What wil the pressure be in the system of the teo test tubes be after achieving mechanical equilibrium? What would the pressure be if it would have been nitrogen and not oxygen that was in the test tubes?(while keeping other conditions the same)/p>

Take an empty cylindrical cup. Turn it upside down and push it beneath a calm water surface. How high will the column of air in the cup be depending on the submersion of the cup?

We have a container of a constant cross section, which contains an ideal gas and a piston at a height of $h$. First we compress the air quickly (practically adiabatically) by moving the piston to a height of $h⁄2$, we hold it there until thermal equilibrium with its surroundings is reached, and then we let it go. To what height will the piton rise immediately? What is the height that it will reach after a very long time? Draw a $pV$ diagram.

A horizontal pipeline with a flowing liquid contains a small bubble of gas. How do the dimensions of this bubble change when it reaches a narrower point of the pipeline? Can you find some applications of this phenomena? What problems could it cause? Assume that the flow is laminar.

A Siberian gas pipeline with a liquefied natural gas needs to be closed. Váňa Vasilijevič decided to do this manually by closing a frictionless valve. What is the work he needed to do so? What is the force he acted on the valve with (choose an appropriate parameter to describe it)? You can imagine the valve as a board that is being inserted into the pipeline (the pipeline is perpendicular to this board). Initially, the pressure inside the pipeline was $p=2MPa$. Its cross-section is square-shaped with a side of length $a=1\;\mathrm{m}$. The board is $d=10\;\mathrm{cm}$ wide, the density of liquefied natural gas is $ρ=480\;\mathrm{kg}⁄m$, and its flow rate is $q=20m3\;\mathrm{s}$.

What is the mass percentage of Earth's atmosphere that escapes to the outer space each year? Assume the atmosphere reaches 10 km above the ground, the pressure is everywhere the same (equal to the pressure at sea level) and it consists of ideal gas at tepmperature 300K whose molecular speeds obey the Maxwell-Boltzmann distribution. Also assume that the gravitational field is homogeneous.