Entropy change when converting water to steam

[doombanana]

Homework Statement

At constant atmospheric pressure, 20g of water at 30C is converted into steam at 250C. Assume the heat capacity of liquid water is constant at 4.2 J/gK and the heat of vaporization at 100C is 2260 J/g. The molar heat capacity of water vapor at constant pressure is given by

$\frac{c_p}{R} = a + bT + CT^2$

where $a= 3.634,{ } b= 1.195*10^{-3} K^{-1},{ } c=1.350*10^{-7} K^{-2}$

Find the entropy change of the water.

Homework Equations

$\Delta S = \frac{dQ}{T}$
$dQ = \int c_p dT$

The Attempt at a Solution

My first thought was just to plug in the given equation for C_p into (1) and integrating, but I'm not sure how the heat of vaporization comes into play.

 

[BruceW]

There are 3 different 'stages' to this problem. You need to think of what they are, then find the entropy change that happens in each stage.