Answer:
a) The equation giving the boiling point of the liquid is [tex]T(z) = 214-\frac{19}{10000}\cdot z[/tex].
b) The boiling point of the liquid at 2400 feet is 209.44 degrees Fahrenheit.
Step-by-step explanation:
a) From the statement of the problem, we understand that boiling point of a liquid is represented by the following linear function in terms of altitude:
[tex]T(z) = T_{1} + \frac{T_{2}-T_{1}}{z_{2}-z_{1}} \cdot (z-z_{1})[/tex] (Eq. 1)
Where:
[tex]T(z)[/tex] - Temperature as a function of altitude, measured in degrees Fahrenheit.
[tex]z[/tex] - Altitude, measured in degrees Fahrenheit.
[tex]T_{1}[/tex], [tex]T_{2}[/tex] - Lower and higher temperatures, measured in degrees Fahrenheit.
[tex]z_{1}[/tex], [tex]z_{2}[/tex] - Lower and higher altitudes, measured in feet.
If we know that [tex]z_{1} = 4400\,ft[/tex], [tex]z_{2} = 8400\,ft[/tex], [tex]T_{1} = 205.64\,^{\circ}F[/tex], [tex]T_{2} = 198.04\,^{\circ}F[/tex], then we find that the equation giving the boiling point of the liquid is:
[tex]T(z) = 205.64-\frac{19}{10000}\cdot (z-4400)[/tex]
[tex]T(z) = 214-\frac{19}{10000}\cdot z[/tex] (Eq. 2)
The equation giving the boiling point of the liquid is [tex]T(z) = 214-\frac{19}{10000}\cdot z[/tex].
b) If we know that [tex]z = 2400\,ft[/tex], then the boiling point of the liquid at such altitude is:
[tex]T(2400) = 214-\frac{19}{10000}\cdot (2400)[/tex]
[tex]T(2400) = 209.44\,^{\circ}F[/tex]
The boiling point of the liquid at 2400 feet is 209.44 degrees Fahrenheit.
