114 SOLUTIONSwhere 0 and 1correspond to the initial and final equilibriumstates of the
system, withsets ofparameters and respectively. In
thiscase, the gas is expanding,thereforesomepositive work is done by the
gas,which indicatesthat theenergy change is negative, and thetemperature
decreases. for anideal gasdepends only on thechange intemperature:
where is the heatcapacity of one mole of thegas at constant volume
(for amonatomic gas The work done by the gasgoesinto
compressing the spring:whereKis the spring constant and is the change of the piston position
(seeFigureS.4.24). On theother hand, whenequilibrium isreached, the
compressionforce of the spring
whereAis the crosssection of the piston. So
where weused the idealgas law for onemole of gas.Substituting(S.4.24.5)
into(S.4.24.3), we have
Notice that is thevolume change of the gas: