An ideal gas is confined to acylinder by a massless piston that is attached to a

Question

    An ideal gas is confined to acylinder by a massless piston that is attached to an ideal spring.Outside the cylinder is a vacuum. The cross-sectional area of thepiston is A. The initial pressure volume and temp of the gas areP0, V0 and T0 and the spring is initially stretched by an amount X0with respect to its unstrained length. The gas is heated so thatits final pressure volume and temp are Pf, Vf and Tf and the springis stretched by an amount Xf with respect to its unstrained length.Assume X0 and Xf are positive variables
A) What is the relation between the magnitude of force required tostretch an ideal spring and amount of the stretch with respect tounstrained length of the spring?
B) What are the magnitudes, F0 and Ff, of the forces that theinitial and final pressures apply to the piston and hence to thespring? express your answer in terms of the pressures andcross-sectional area of the piston.
C) According to the ideal gas law, how are the initialpressure,volume and temperature related to the final pressure,volume and temperature?
D) How is the final volume related to the initial volume, the crosssectional area of the piston and the initial and final amounts bywhich the spring is stretched? account for your answer

Problem: The initial temperature and volume of the gas described inthe Concept questions above are 273 K and 6.00 *10^ -4 m^3. theintial and final amounts by which the spring is stretched are0.0800m and 0.1000 m. The cross sectional area of the piston is2.50 *10^ -3 m^2. What is the final temp of the gas?

HELP!! answer to any question will be greatlyappreciatedd!!!! An ideal gas is confined to acylinder by a massless piston that is attached to an ideal spring.Outside the cylinder is a vacuum. The cross-sectional area of thepiston is A. The initial pressure volume and temp of the gas areP0, V0 and T0 and the spring is initially stretched by an amount X0with respect to its unstrained length. The gas is heated so thatits final pressure volume and temp are Pf, Vf and Tf and the springis stretched by an amount Xf with respect to its unstrained length.Assume X0 and Xf are positive variables
A) What is the relation between the magnitude of force required tostretch an ideal spring and amount of the stretch with respect tounstrained length of the spring?
B) What are the magnitudes, F0 and Ff, of the forces that theinitial and final pressures apply to the piston and hence to thespring? express your answer in terms of the pressures andcross-sectional area of the piston.
C) According to the ideal gas law, how are the initialpressure,volume and temperature related to the final pressure,volume and temperature?
D) How is the final volume related to the initial volume, the crosssectional area of the piston and the initial and final amounts bywhich the spring is stretched? account for your answer

Problem: The initial temperature and volume of the gas described inthe Concept questions above are 273 K and 6.00 *10^ -4 m^3. theintial and final amounts by which the spring is stretched are0.0800m and 0.1000 m. The cross sectional area of the piston is2.50 *10^ -3 m^2. What is the final temp of the gas?

HELP!! answer to any question will be greatlyappreciatedd!!!!

Explanation / Answer

(a)    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 = Po A    Ff = PfA     (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 = (Pf Vf/ Po Vo) To

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