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 crosssection of which is A=2 dm^{2}. 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 V_{0}=8 dm^{3}. The external pressure is p_{0}=10^{5} Pa, g=10 m/s^{2}. 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 v_{0}=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 V_{0} to V_{1}=18 dm^{3}.
b) Determine the heat transferred by the electric heating element to the expanding gas in the process.
(5 pont)
Deadline expired on 12 January 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, KunságiMáté 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 solutions. 
