A cylinder having a piston restrained by a linear spring $($of spring constant $15k\frac{N}{m})$ contains $0\mathrm{.}5$ kg of saturated vapor water at $120C,$ as shown in the figure. Heat is transferred to the water, causing the piston to rise. If the piston's cross$-$sectional area is $0\mathrm{.}05m^2$ and the pressure varies linearly with volume until a final pressure of $500$ kPa is reached, find the final temperature in the cylinder and the heat transfer for the process. $($Ans$.803C,587kJ)$

Problem $28$