Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
 Already signed up? New to KöMaL?

# Problem P. 4852. (May 2016)

P. 4852. There is a frictionlessly moveable piston in a thermally insulated vertical cylinder closed at both of its ends and of cross section $\displaystyle A=1~{\rm dm}^2$. Two springs (which are both designed for compression and tension) are attached to the piston and to the two bases of the cylinder. The unstretched lengths of the springs are $\displaystyle \ell_1=3~{\rm dm}$ and $\displaystyle \ell_2=5~{\rm dm}$, whilst their spring constants are $\displaystyle D_1=1000$ N/m and $\displaystyle D_2=1500$ N/m. Bellow the piston there is air, the pressure of which initially is $\displaystyle p_1=4\cdot10^4$ Pa, whilst above the piston there is vacuum. Initially the distances between the piston and the bases of the cylinder are $\displaystyle d_1=5~{\rm dm}$ and $\displaystyle d_2=4~{\rm dm}$.

$\displaystyle a)$ Determine the mass of the piston.

$\displaystyle b)$ The air inside cylinder is slowly heated. By what factor should the absolute temperature of the air be raised in order that the piston moves up 10 cm?

$\displaystyle c)$ How much heat is added to the gas during the heating process?

(5 pont)

Deadline expired on June 10, 2016.

### Statistics:

 48 students sent a solution. 5 points: Asztalos Bogdán, Balogh Menyhért, Büki Máté, Csorba Benjámin, Édes Lili, Fajszi Bulcsú, Fehér 169 Szilveszter, Forrai Botond, Ghada Alshalan, Iván Balázs, Jakus Balázs István, Kovács Péter Tamás, Körmöczi Dávid, Krasznai Anna, Marozsák Tóbiás , Molnár Mátyás, Németh Flóra Boróka, Olosz Adél, Páhoki Tamás, Sal Kristóf, Sallai Krisztina, Szántó Benedek, Szentivánszki Soma , Tibay Álmos, Tomcsányi Gergely. 4 points: Bartók Imre, Bekes Nándor, Berke Martin, Csire Roland, Csuha Boglárka, Di Giovanni András, Farkas Domonkos, Fekete Balázs Attila, Kavas Katalin, Kormányos Hanna Rebeka, Kovács 526 Tamás, Mány Bence, Németh 777 Róbert, Pataki 245 Attila, Pázmán Előd, Pszota Máté, Simon Dániel Gábor, Tófalusi Ádám, Varga-Umbrich Eszter, Wiandt Péter. 3 points: 2 students. 1 point: 1 student.

Problems in Physics of KöMaL, May 2016