Question

The relationship between altitude and the boiling point of a liquid is linear. At an altitude of 8400 ​ft, the liquid boils at 198.04°F. At an altitude of 4400 ​ft, the liquid boils at 205.64°F. Write an equation giving the boiling point b of the​ liquid, in degrees​ Fahrenheit, in terms of altitude​ a, in feet. What is the boiling point of the liquid at 2400 ​ft?

Answer 1

Answer:

a) The equation giving the boiling point of the liquid is $T(z) = 214-\frac{19}{10000}\cdot z$.

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:

$T(z) = T_{1} + \frac{T_{2}-T_{1}}{z_{2}-z_{1}} \cdot (z-z_{1})$ (Eq. 1)

Where:

$T(z)$ - Temperature as a function of altitude, measured in degrees Fahrenheit.

$z$ - Altitude, measured in degrees Fahrenheit.

$T_{1}$, $T_{2}$ - Lower and higher temperatures, measured in degrees Fahrenheit.

$z_{1}$, $z_{2}$ - Lower and higher altitudes, measured in feet.

If we know that $z_{1} = 4400\,ft$, $z_{2} = 8400\,ft$, $T_{1} = 205.64\,^{\circ}F$, $T_{2} = 198.04\,^{\circ}F$, then we find that the equation giving the boiling point of the liquid is:

$T(z) = 205.64-\frac{19}{10000}\cdot (z-4400)$

$T(z) = 214-\frac{19}{10000}\cdot z$ (Eq. 2)

The equation giving the boiling point of the liquid is $T(z) = 214-\frac{19}{10000}\cdot z$.

b) If we know that $z = 2400\,ft$, then the boiling point of the liquid at such altitude is:

$T(2400) = 214-\frac{19}{10000}\cdot (2400)$

$T(2400) = 209.44\,^{\circ}F$

The boiling point of the liquid at 2400 feet is 209.44 degrees Fahrenheit.