Question

In the mid-nineteenth century, explorers used the boiling point of water to estimate altitude. The boiling temperature of water (in °F) can be approximated by the model T = -1.83a+212, where a is the altitude in thousands of feet. Determine the temperature at which water boils at an altitude of 5000 ft. Round your answer to the nearest hundredth.

a. 184.28°F
b. 183.91°F
c. 183.56°F
d. 183.22°F

Answer 1

Using the provided model, the boiling temperature of water at an altitude of 5000 ft is calculated to be approximately 202.85°F. This value is determined by substituting the altitude into the temperature formula, accounting for the decrease in boiling point at higher elevations due to lower atmospheric pressure.

Step-by-step explanation:

To determine the boiling temperature of water at an altitude of 5000 ft using the model T = -1.83a + 212, where a is the altitude in thousands of feet, we first convert 5000 feet to thousands of feet (which is 5).

Substituting the value of a into the model:

• T = -1.83(5) + 212
• T = -9.15 + 212
• T = 202.85°F

Hence, the temperature at which water boils at an altitude of 5000 ft is approximately 202.85°F. This result is not found in the choices provided, so it seems there might be a discrepancy in the question or the provided model.

The lower boiling point of water at higher altitudes such as 5000 ft compared to sea level is a result of the reduced atmospheric pressure found at these elevations, which affects the boiling temperature of water significantly.