Chapter SH, Problem 2.7MPS

To determine

To calculate:To determine the temperature change from sea level to the highest point for each mountain given below, when for every $1000$ feet above Earth’s surface, air temperature decreases by $5°F$ .

Answer to Problem 2.7MPS

The table with change in temperature is shown below −

Mountain	Highest Point$\left(ft\right)$	Temperature Change$\left(°F\right)$
Mt. McKinley	$20,320$	$101.6$
Mt. St. Elias	$18,008$	$90.04$
Mt. Foraker	$17,400$	$87$

Explanation of Solution

Given information:

For every $1000$ feet above Earth’s surface, air temperature decreases by $5°F$ .

Table:

Calculation:

Given:

For every $1000$$feet$ above Earth’s surface, air temperature decreases by $5°F$ .

Table:

Since, for every 1000 $feet$ , air temperature decreases by $5°F$ .

So, for every $1$$feet$ , air temperature decreases by ${\left(\frac{5}{1000}\right)}^{°}F$ .

For every $1$$feet$ , air temperature decreases by ${\left(0.005\right)}^{°}F$ .

Now, the highest point of Mt. McKinley is $20,320$$ft$ ; so the air temperature would decrease by ${\left(0.005\times 20,320\right)}^{°}F$ .

Hence, the decrease in air temperature for Mt. McKinley at $20,320$$ft$ is $101.6°F$ .

Similarly, calculating the decrease in air temperature for all the other mountains, we have:

Highest point of Mt. St. Eliasis $18,008$$ft$ ; so the air temperature would decrease by ${\left(0.005\times 18,008\right)}^{°}F$ .

Hence, the decrease in air temperature for Mt. McKinley at $18,008$$ft$ is $90.04°F$ .

Highest point of Mt. Forakeris $17,400$$ft$ ; so the air temperature would decrease by ${\left(0.005\times 17,400\right)}^{°}F$ .

Hence, the decrease in air temperature for Mt. McKinley at $17,400$$ft$ is $87°F$ .

Conclusion:

The table with change in temperature is shown below −

Mountain	Highest Point$\left(ft\right)$	Temperature Change$\left(°F\right)$
Mt. McKinley	$20,320$	$101.6$
Mt. St. Elias	$18,008$	$90.04$
Mt. Foraker	$17,400$	$87$