The summit of Mount Whitney, in California, is 3660 m higher than a point in the foothills. Assu

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The summit of Mount Whitney, in California, is 3660 m higher...

The summit of Mount Whitney, in California, is $3660 \mathrm{m}$ higher than a point in the foothills. Assume that the atmospheric lapse rate in the Mount Whitney area is the same as the global average of $-6.5^{\circ} \mathrm{C} / \mathrm{km} .$ What is the temperature of the summit of Mount Whitney when eager hikers depart from the foothill location at a temperature of $30^{\circ} \mathrm{C}$ ?

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Key Concepts

Unit Conversion in Altitude Measurements

When applying concepts like the atmospheric lapse rate, it is crucial to perform unit conversions to ensure consistency. Since the lapse rate is typically expressed per kilometer, any altitude difference given in other units, such as meters, must be converted appropriately to accurately calculate the corresponding temperature change.

Temperature Difference Calculation

Calculating temperature differences using the lapse rate involves multiplying the vertical distance (after appropriate unit conversion) by the lapse rate. This method provides a straightforward linear estimation of the temperature at a different altitude and is a common tool in environmental science, aviation, and outdoor planning.

Atmospheric Lapse Rate

The atmospheric lapse rate is the rate at which air temperature decreases with an increase in altitude in the troposphere. This linear relationship, often averaged as -6.5°C per kilometer, is fundamental in meteorology for estimating temperature changes over vertical distances, influencing weather prediction, climate studies, and understanding atmospheric stability.

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