$7\mathrm{.}118.$ Thermal Expansion of an Ideal Gas. $($a$)$ The pressure $p,$

volume $V,$ number of moles $n,$ and Kelvin temperature $T$ of an

ideal gas are related by the equation $pV=nRT,$ where $R$ is a con$-$

stant. Prove that the coefficient of volume expansion for an ideal

gas is equal to the reciprocal of the Kelvin temperature if the

expansion occurs at constant pressure. $($b$)$ Compare the coeffi$-$

cients of volume expansion of copper and air at a temperature of

$20C.$ Assume that air may be treated as an ideal gas and that the

pressure remains constant.