Concept Question An ideal gas is confined to a cylinder by a massless piston tha
ID: 1745668 • Letter: C
Question
Concept Question
An ideal gas is confined to a cylinder by a massless piston that isattached to an ideal spring. Outside the cylinder is vacuum. Thecross-sectional area of the piston is A. the intail pressure,volume, and temperature of the gas are , respectively, P0, V0, andT0, and the spring is intially strectched by the amount x0 withrespect to its unrestrained length. The gas is heated, so that itsfinal pressure, volume, and temperature are Pf,Vf, and Tf and thespring is strectched by an amount xf with respect to unstrainedlength. Assume the x0 and xf are positive variables. (a) What isthe realation between the magnitude of the force required tostretch an ideal spring and the amount of the stretch with respectto the unrestrained length of the spring? (b) What are themagnitudes, Fo and Ff, of teh forces thatthe intial and finalpressures apply to the piston and, hence, to the spring? Expressyour answers in terms of the pressures and the cross-sectional areaof teh piston. (c) According to the ideal gas law, how are theintial pressure, volume, and temperature related to the finalpressure, volume, and temperature? (d) How is the final volumerelated to teh intial volume, the cross-sectional area of thepiston, and the intial and final amounts by which the spring isstretched? Account for your answer
Problem
Question Details:Concept Question
An ideal gas is confined to a cylinder by a massless piston that isattached to an ideal spring. Outside the cylinder is vacuum. Thecross-sectional area of the piston is A. the intail pressure,volume, and temperature of the gas are , respectively, P0, V0, andT0, and the spring is intially strectched by the amount x0 withrespect to its unrestrained length. The gas is heated, so that itsfinal pressure, volume, and temperature are Pf,Vf, and Tf and thespring is strectched by an amount xf with respect to unstrainedlength. Assume the x0 and xf are positive variables. (a) What isthe realation between the magnitude of the force required tostretch an ideal spring and the amount of the stretch with respectto the unrestrained length of the spring? (b) What are themagnitudes, Fo and Ff, of teh forces thatthe intial and finalpressures apply to the piston and, hence, to the spring? Expressyour answers in terms of the pressures and the cross-sectional areaof teh piston. (c) According to the ideal gas law, how are theintial pressure, volume, and temperature related to the finalpressure, volume, and temperature? (d) How is the final volumerelated to teh intial volume, the cross-sectional area of thepiston, and the intial and final amounts by which the spring isstretched? Account for your answer
Problem
The intial temperature and volume of the gas described in theconcept questions are 273 K and 6.00 x 10 ^-4 m^3. The intail andfinal amounts by which the spring is stretched are, respectively,0.0800 and 0.1000 m. The cross-sectional area of the piston is 2.50x 10^-3 m^2. What is the final temperature of the gas?Explanation / Answer
the force Fapplied that mustbe applied to stretch an ideal spring by an amount x with respectto its unstrained length is given by Fapplied = k x where k is the spring constant (b) pressure is the magnitude of the forceapplied perpendicularly to a surface divided by the area of thesurface thus, the magnitudes of the forces that the initialand final pressures apply to the piston (and, therefore, to thespring) are given by Fo = PoA Ff =Pf A (c) the ideal gas law is PV = nRT since the number of moles is constant, thisequation can be written as (P V / T) = n R thus, the value of (P V / T) isthe same initially and finally, and we can write Po Vo /To = Pf Vf /Tf (d) the final volume is the initial volume plusthe amount by which the volume increases as the springstretches the increased volume due to the additionalstretching is A (xf - xo) so we get that Vf = Vo + A(xf - xo) the final temperature canb be obtainedfrom Tf = (PfVf / PoVo) To Hope this helpsu! Hope this helpsu!Related Questions
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