IOM 2016, Блиц — Задача 79

Olympiad of Metropolises, Moscow. Blitz Contest, September, 5 · 5 септември 2016 г.

Условие

The answer should be given in SI-units and rounded to the nearest integer, unless otherwise is stated. $g = 10$ m/s$^2$.

In figure below, a thermally insulated vertical cylinder with height $L = 20$ meter and cross sectional area $A = 0.1$ m$^2$ is planted on the ground. The top part of the cylinder is open to the atmosphere with atmospheric pressure $P_{out} = 10^5$ Pa. The bottom part of the cylinder is closed. The lower half of the cylinder contains a high pressure air under a piston with mass $M_p = 300$ kg. Initially, the piston is held in place by a force so that it does not move. The data of the enclosed air is: pressure $P_1 = 3 \times 10^5$ Pa, volume $V_1 = 1$ m$^3$, temperature $T_1 = 300$ K, and heat capacity ratio $\gamma = c_p/c_v = 1.4$.

The piston is then released such that the enclosed air starts to expand and the piston moves upward. Assume in the subsequent process that the pressure and temperature of the enclosed air are uniform. What is the velocity of the piston at the top of the cylinder? The gravitational potential energy of the air can be ignored. $g = 10$ m/s$^2$. The answer should be given in m/s and rounded to the nearest integer.

Решение

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Оригинал в Архива: blitz.pdf