$19\mathrm{.}6($a$)$ A rigid vessel of volume $0\mathrm{.}58m^3$ contains $1$ kg of steam at a pressure of $300{10}^2\frac{N}{m^2}.$ Evaluate the specific volume, the temperature, the dryness fraction, the internal energy and the enthalpy of the steam.

$($b$)$ Heat transfer to the steam causes its temperature to rise to $160C.$ Show the path of this process on a sketch of the $pv$ diagram and evaluate the pressure, the increase in enthalpy, the increase in internal energy of the steam and the heat transfer. Evaluate also the pressure at which the steam becomes dry$-$saturated.