Water + Water Vapor - Can I use ideal gas law?

[bphysics]

Homework Statement

Sealed container which is used to heat 200 kg water is initially at 25 degrees C. Since the container is sealed, the water remains in saturated state while its temperature and pressure increases. The remaining volume of the container is filled with water vapor at the same temperature and pressure. There is a pressure safety valve on the container.

a) If the max allowed water temperature is 150 degrees C, at what pressure should the safety value open?
b) How much energy is needed to increase temperature of water from 25 degrees C to 150 degrees C? You can neglect mass of water vapor and assume closed system containing only 200 kg of water.

Homework Equations

PV = mRT where m = R/M (M = molar mass).

The Attempt at a Solution

I cannot find a definitive source which will confirm that I can use the ideal gas law on this problem. In addition, water vapor and water have different specific heats at a constant pressure and I must account for the total pressure within the system.

Do I need to split the system into two separate parts and calculate the pressure in each individual part as the temperature is raised? This doesn't seem logical to me -- the pressure valve needs to be set based on what the total pressure of the system will be...

Any advice? Just not sure how to attack this guy.

 

[Dickfore]

No, there is a Pressure vs. Temperature curve for the phase transition liquid - gas. This is the relation you need.

 

[bphysics]

No, there is a Pressure vs. Temperature curve for the phase transition liquid - gas. This is the relation you need.

The problem note that the water remains in a saturated state. I would assume this indicates it does not become a gas, is this correct?

 

[Dickfore]

Saturated vapor is vapor in equilibrium with the liquid phase underneath it. It has the same pressure and temperature.

 

[bphysics]

Is it possible for the ideal gas law to be used in any way for this problem? I am simply surprised, because the core of the chapter which contains this problem discusses the ideal gas law and the book's tables provide C_p and C_v for both saturated water/steam in both liquid and vapor forms.

My own notes mention that the professor noted that water vapor is NOT an ideal gas, so I guess the book does not have a solid explanation of how to solve this problem.

 

[Dickfore]

You need to use something like this:

http://www.engineeringtoolbox.com/water-vapor-saturation-pressure-d_599.html

As you can see, the dependence is non-linear and, therefore, inconsistent with the ideal gas law.