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

a) The equation giving the boiling point of the liquid is
`T(z) = 214-(19)/(10000)\cdot z`.

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

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) + (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-(19)/(10000)\cdot (z-4400)`

`T(z) = 214-(19)/(10000)\cdot z` (Eq. 2)

The equation giving the boiling point of the liquid is
`T(z) = 214-(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-(19)/(10000)\cdot (2400)`

`T(2400) = 209.44\,^(\circ)F`

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