What is the pressure on Pike's Peak above Denver, CO?

[enviroengnhopeful]

At ground level in Denver, Colorado, the atmospheric pressure and temperature are 83.2 kPa and 25 degrees Celsisus. Calculate the pressure on Pike's Peak at an elevation of 2690 m above the city assuming an incompressible atmosphere.

 

[FredGarvin]

Two things:

- Homework belongs in the homework section.
- You must show some attempt at a solution. We will not just give you an answer.

 

[ravenprp]

To calculate the pressure on Pike's Peak, we can use the formula P = P0 * e^(-Mgh/RT), where P is the pressure at the given elevation, P0 is the pressure at ground level, M is the molar mass of air, g is the acceleration due to gravity, h is the elevation difference, R is the gas constant, and T is the temperature.

First, we need to convert the temperature from degrees Celsius to Kelvin by adding 273.15, giving us a temperature of 298.15 K.

Next, we need to calculate the elevation difference between Denver and Pike's Peak. Since Pike's Peak is 2690 m above Denver, the elevation difference (h) is 2690 m.

The molar mass of air (M) is approximately 28.97 g/mol, the acceleration due to gravity (g) is 9.8 m/s^2, and the gas constant (R) is 8.314 J/mol*K.

Plugging in these values, we get:

P = (83.2 kPa) * e^(-[(28.97 g/mol)(9.8 m/s^2)(2690 m)] / [(8.314 J/mol*K)(298.15 K)])

Simplifying, we get:

P = (83.2 kPa) * e^(-0.000112)

P = (83.2 kPa) * 0.999888

P = 83.19 kPa

Therefore, the pressure on Pike's Peak above Denver, CO is approximately 83.19 kPa. This is slightly lower than the pressure at ground level in Denver due to the decrease in atmospheric density at higher elevations.