[Giger]

A discussion among us firefighters. We all agree that when water       
turn to vapor at 100 celsius it expands 1700 times. The question we don't agree on is what happens with the volume if the vapor gets heated above 100 C. Self ignition for wood is around 550 C. Cooling this whit water will make the water vapor hotter than 100C. Some had learned that vapor at 400C is 2500 times the volume.  Some argued whit PV=nRT and got around 3500 times the volume. And yet another group (the majority) tough that the temperature shouldn't make any difference.  Anyone out there want to help us set this straight?

[curiouscat]

I'll try.

International steam tables reveal the following specific volumes in m³/kg:

(1) Liquid H2O at 1 atm P & T=20°C, say as a reference point: 1.002×10^-3 m³/kg

(2) Saturated vapor H2O at 1 atm P (i.e. T=100°C): 1.673 m³/kg

(3) Assuming 400°C as the steam temp. in your wood fire the steam will be superheated & not saturated (since P=1 atm)  : 3.102 m³/kg

Hence your normal expansion from water at 20°C to saturated steam at 100°C seems ~1670

If water at 20°C OTOH turned to steam at 400°C I get an expansion factor of ~3096

I could be wrong though. Let's see if someone can verify my calculations.

[curiouscat]

Some argued whit PV=nRT and got around 3500 times the volume.

Let's try that:

ρ = PM / (RT)

P=1.01325×10 ⁵

M=18×10 ^-3

R=8.314

T = 400 + 273

Specific Volume = 1/ρ

Comes to 3.078 m³/kg

That'd  yield an expansion factor of ~3072 so pretty close to that 3096 we had from the Steam Table approach.

The steam table approach I like better than the Ideal Gas Law because the latter is always an approximation.