Problem P. 4121. (December 2008)

P. 4121. A piston, which can move without friction, closes a sample of Helium in a vertical, thermally insulated cylinder, which is closed at its bottom, and the cross-section of which is A=2 dm². Above the piston there is a fixed stand to which an unstretched spring of spring constant D=2000 N/m is attached, whose bottom end is at a distance of d=2 dm from the piston when the volume of the gas is V₀=8 dm³. The external pressure is p₀=10⁵ Pa, g=10 m/s². The gas confined in the cylinder is heated with an electric heating element which is automatically controlled such that the piston is continuously moving with a constant speed of v₀=5 cm/s.

a) Determine and plot the instantaneous power of the heating element as a function of the time, while the volume of the gas increases from V₀ to V₁=18 dm³.

b) Determine the heat transferred by the electric heating element to the expanding gas in the process.

(5 pont)

Deadline expired on January 12, 2009.

Statistics:

66 students sent a solution.
5 points:	Bartha Zsolt, Czeller Ildikó, Fridrich Veronika, Hegedűs Csaba, Illés Dorottya, Maknics András, Nagy 111 Miklós, Vuchetich Bálint.
4 points:	Borsos 607 Zalán, Csányi Gergely, Fonai Dániel, Galzó Ákos Ferenc, Harnos Balázs, Hartstein Máté, Jakab Dávid, Kaposvári István, Kovács 235 Gábor, Kovács Benjámin, Krämer Zsolt, Kungl 008 Ákos, Kunsági-Máté Éva, Lovas Lia Izabella, Mayer Martin János, Najbauer Eszter Éva, Németh Gábor , Patartics Bálint, Pázmán Koppány, Rácz Viktor, Sós Attila Róbert, Szabó 928 Attila, Trényi Róbert.
3 points:	14 students.
2 points:	7 students.
1 point:	9 students.
0 point:	3 students.
Unfair, not evaluated:	2 solutionss.

Problems in Physics of KöMaL, December 2008