Expansion of steam: When water changes to steam, its volume increases rapidly. At a normal atmospheric pressure of 14.7 pounds per square inch, water boils at 212 degrees Fahrenheit and expands in...

Expansion of steam: When water changes to steam, its volume increases rapidly. At a normal atmospheric pressure of 14.7 pounds per square inch, water boils at 212 degrees Fahrenheit and expands in volume by a factor of 1700 to 1. But when water is sprayed into hotter areas, the expansion ratio is much greater. This principle can be applied to good effect in fire fighting. The steam can occupy such a large volume that oxygen is expelled from the area and the fire may be smothered. The table below shows the approximate volume, in cubic feet, of 50 gallons of water converted to steam at the given temperatures, in degrees Fahrenheit.

a. Make a linear model of volume V as a function of T.

b. If one fire is 100 degrees hotter than another, what is the increase in the volume of steam produced by 50 gallons of water?

c. Calculate V (420) and explain in practical terms what your answer means.

d. At a certain fire, 50 gallons of water expanded to 14,200 cubic feet of steam. What was the temperature of the fire?