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Problem P. 4722. (March 2015)

P. 4722. There are two cylinders of cross section \(\displaystyle A=2~\rm{dm}^2\) at rest on a frictionless, horizontal surface. The pistons of the cylinders can move easily and they are connected with a rigid rod. Each cylinder is connected to an unstretched spring. The values of the spring constant of the springs are \(\displaystyle D_{\rm b}=24\) kN/m, and \(\displaystyle D_{\rm j}=16\) kN/m. The volume of the air enclosed in the left, insulated cylinder is \(\displaystyle V_{\rm 0b}=20~{\rm dm}^3,\) and that of in the right cylinder is \(\displaystyle V_{\rm 0j}=30~{\rm dm}^3\), and the initial temperature of both gases is \(\displaystyle T_0=300\) K. The temperature of the gas in the left cylinder is increased to \(\displaystyle T_{\rm b}=1200\) K. The ambient air pressure is \(\displaystyle p_0=10^5\) Pa.

\(\displaystyle a)\) What is the displacement of the two cylinders and the piston with respect to the ground if the temperature of the gas in the right cylinder is kept at its initial value?

\(\displaystyle b)\) What are the final values of the volume of the two samples of gas?

\(\displaystyle c)\) How much heat was released by the heating element which heated the gas in the left cylinder?

(5 pont)

Deadline expired on 10 April 2015.


Statistics:

33 students sent a solution.
5 points:Asztalos Bogdán, Balogh Menyhért, Blum Balázs, Csathó Botond, Holczer András, Iván Balázs, Jakus Balázs István, Olosz Balázs, Öreg Botond.
4 points:Bekes Nándor, Bugár 123 Dávid, Di Giovanni Márk, Fekete Panna, Forrai Botond, Lőrincz Zoltán, Mándoki László, Marosvári Kristóf, Németh Flóra Boróka, Sal Kristóf, Szentivánszki Soma , Szépfalvi Bálint, Varga-Umbrich Eszter, Varju Ákos.
3 points:2 students.
2 points:8 students.

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