$4\mathrm{.}8$ A simple system is held in a rigid, constant$-$volume container. The system experiences an infinitesimal change of its pressure rises. The question is whether during this constant$-$volume pressurization process the system is being cooled or heated. Show that the constant$-$volume pressurization is the result of heating if the system$$s properties vary such that $$ c v$>0$ where cv$,$k$,$and$$ are the specific heat at constant volume,the isothermal compressibility, and the volumetric coefficient of thermal expansion, respectively.