Write the equations defining thermal expansion coefficient $()$ and isothermal compressibility $().$

$($i$)$ Obtain simplified expressions for $()$ and $()$ for an ideal gas. Show how you derive the simplified

expressions stepwise.

$($ii$)$ For water $=4\mathrm{.}94{10}^{-6}at{m}^{-1}$ at $20C$ and $1$atm. Calculate the change in volume of $50c{m}^3$ water if an

extra $1000$atm of pressure is applied on it at constant temperature.