Calculate the amount of work necessary for the reversible compression of steam from $1$ bar $t\frac{10}{b}ar.$ The compression is to take place in a cylinder fitted with a weightless piston at the constant temperature of $500C.$ Under these conditions we have a superheated vapor. Assum that steam may be treated as an ideal gas.

Report your answer in units of $k\frac{J}{k}g$ using three decimal places. For conversion, note that the molar mass of water is $18\mathrm{.}015\frac{g}{m}ol.$