A cylinder A, having Va = 30 litres of an ideal monoatmoicgas, is connected to a second cylinder, B, of circularcross-section, as shown in Fig. 3.16 of the book(shown below).Cylinder B is fitted with a piston of diameter 10 cm, which slideswithout friction or leaking. Initially: Pa = 10 MPa, Ta = 300 K, Vb= 0, and the compression force on the spring is zero. The springobeys Hooke's law and has a stiffness k = 10^5 Nm^-1. Remember thatthe work done by such a spring is: Wspring = -k(Xf^2 - Xo^2)/2,with x = 0 the equilibruim position of the spring.
The valve, V, is opened slowly and the gas leaks through fromA to B, compressing the spring. Equilibrium is eventuallyestablished again at a temperature of 300 K throughout all parts ofthe system.
(a) Calculate the distance by which the spring is compressedin the final equilibrium state.
(b) Determine the work done on the gas.
(c) Calculate the total heat transferred to the gas duringthis process.
Consider now there is an externally applied force holding thepiston hard against the left-hand side of volume B while the valveis opened fully. The external force is then gradually reducedallowing the piston to move slowly while the gas expandsisothermally, compressing the spring.
(d) Calculate the amount by which the spring is ultimatelycompressed.
(e) Establish the work of compression of the spring and thework done by the externally applied force.
(f) Determine the heat transferred to the gas during thisprocess.
WHAT I KNOW:
The back of the book provides all the answers but does notexplain how to get them.
it lists:
(a) .6684 m
(b) -22.34 kJ
(c) 22.34 kJ
(d) .6684 m
(e) 22.34 kJ (on spring), -48.38 kJ (on gas), and 26.04 (extforce)
(f) 48.38 kJ
I understand the answers for b and c given a - since thechange in energy is 0 so W = -Q. and putting in .6684 so Xf and 0for Xo into the Wspring equation you get the 22.34 kJ answer.
I can't however find how to calculate the compression. I haveused PV=NRT and manipulated it to high heaven and just cant getit.
Parts d through f I havn't touched since I havn't been able tofind a
