$4\mathrm{.}8$ Asimple systemis held ina rigid, constant$-$volume container. The systemexperiencesan infinitesimal changeof stateduringwhich its pressure rises. Thequestion iswhether during this constant$-$volume pressurizationprocess the systemis being cooledor heated. Show that theconstant$-$volumepressurizationis theresultofheatingif the system$$spropertiesvarysuchthat $$ cv$>0$ wherecv,k$,$and$$arethespecificheatatconstantvolume$,$theisothermal compressibility, and thevolumetriccoefficient of thermal expansion, respectively.