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.