Problem $2(40\%).$

A piston$-$cylinder assembly contains $2$ kg of water at $120C$ and $1$ bar $.$ The water is

compressed to a saturated vapor state where the pressure is $4$ bar. During

compression, there is a heat transfer of energy from the water to its surroundings

having a magnitude of $200$kJ$.$ Neglecting changes in kinetic energy and potential

energy, determine the work, in kJ $,$ for the process of the water.