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Problem P. 4984. (December 2017)

P. 4984. Express, in terms of the ratio of the specific heat capacities, \(\displaystyle \kappa=c_p/c_V\), what portion of the absorbed heat by a sample of gas, expanding at constant pressure, is the work done by the expanding gas.

(3 pont)

Deadline expired on January 10, 2018.


Sorry, the solution is available only in Hungarian. Google translation

Megoldás. A felvett hő:

\(\displaystyle Q =mc_p \Delta T,\)

a belső energia megváltozása:

\(\displaystyle \Delta E=mc_V \Delta T.\)

Az I. főtétel szerint

\(\displaystyle Q=\Delta E+W',\)

azaz

\(\displaystyle W'=m\left(c_p-c_V\right)\Delta T.\)

Innen

\(\displaystyle \frac{W'}{Q }= \frac{c_p-c_V}{c_p }=1-\frac{1}{\kappa}.\)


Statistics:

40 students sent a solution.
3 points:Andorfi István, Apagyi Dávid, Balog 518 Lóránd, Békési Péter, Bukor Benedek, Czett Mátyás, Debreczeni Tibor, Édes Lili, Ferenczi Lajos Szabolcs, Garamvölgyi István Attila, Guba Zoltán, Jánosik Áron, Kiss Dániel Márk, Kiszli Zalán, Lipták Gergő, Markó Gábor, Máth Benedek, Merkl Gergely, Molnár 957 Barnabás, Molnár Mátyás, Morvai Orsolya, Ónodi Gergely, Pszota Máté, Rusvai Miklós, Schneider Anna, Surján Botond, Szakály Marcell, Tafferner Zoltán, Tófalusi Ádám, Turcsányi Máté.
2 points:Baji Bence, Balaskó Dominik, Balogh Tamás, Boros Máté, Pácsonyi Péter, Stefán Boglárka Abigél, Viczián Anna.
1 point:3 students.

Problems in Physics of KöMaL, December 2017