A $10-$m$-$high cylinder, with a cross$-$sectional area of $0\mathrm{.}1$ m$2,$ has a massless thin piston at the

bottom with water at $20$C on top of it$,$ similar to Figure below. The air at $300$ K$,$ V $=0\mathrm{.}3$ m$3$ is

heated so that the piston moves up$,$ spilling the water out over the side. Find the total heat transfer

to the air when all the water has been pushed out. Consider a linear relationship between pressure

and volume for air. Consider air an ideal gas. $(25$ pt$)$

Hint $1$: Properties of liquids is a function of temperature.

Hint $2$: P$0$ is the atmosphere pressure equal to $101\mathrm{.}325$ kPa