Calculate the pressure at this altitude?

In summary, to calculate the pressure at an altitude of 2.0 km, assuming a US standard atmosphere with dry air and a molecular weight of 29.0 × 10^-3 kg/mol, one must use the following equation: p(2000)=(1-lapse rate z/288)9.8x10^-3/R*lapse rate, where the temperature T at altitude z can be found using the equation T=T0-Lz and the equation for dp/dz is dp/dz=-ρg, with ρ being the air density at temperature T and pressure p. Combining these equations results in a differential equation for dp/dz in terms of p and z.
  • #1
Clueless help
2
0

Homework Statement


Calculate the pressure at this altitude. Assume a US standard atmosphere.
an air parcel rises from sea level, where the pressure is 1.01 × 10^5Pa, to an altitude of 2.0 km.
A.calculate the pressure at this altitude. Assume a US standard atmosphere,
take the air to be dry and take the molecular weight of air as 29.0 × 10^-3 kg/mol.

Homework Equations



A.calculate the pressure at this altitude. Assume a US standard atmosphere,
take the air to be dry and take the molecular weight of air as 29.0 × 10^-3 kg/mol.

B.calculate the temperature of the air parcel at this altitude. Take the
values of the heat capacities from above.

The Attempt at a Solution


Dont even know how to start should the equation be along the lines of; p(2000)=(1-lapse rate z/288)9.8x10^-3/R*lapse rate?
 
Last edited by a moderator:
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  • #2
Sorry if this is a mess guys its my first post any help would be greatly appreciated, doing atmospheric psychs for the the first time in college and having a hard time. Thanks
 
  • #3
Clueless help said:

Homework Statement


Calculate the pressure at this altitude. Assume a US standard atmosphere.
an air parcel rises from sea level, where the pressure is 1.01 × 10^5Pa, to an altitude of 2.0 km.
A.calculate the pressure at this altitude. Assume a US standard atmosphere,
take the air to be dry and take the molecular weight of air as 29.0 × 10^-3 kg/mol.

Homework Equations



A.calculate the pressure at this altitude. Assume a US standard atmosphere,
take the air to be dry and take the molecular weight of air as 29.0 × 10^-3 kg/mol.

B.calculate the temperature of the air parcel at this altitude. Take the
values of the heat capacities from above.

The Attempt at a Solution


Dont even know how to start should the equation be along the lines of; p(2000)=(1-lapse rate z/288)9.8x10^-3/R*lapse rate?

Write an equation for the temprature T at altitude z, given that the temperature at the surface is 288, and the lapse rate is L.

What is the equation for dp/dz in terms of air density and g?

What is the equation for air density at temperature T and pressure p?

Combine all this into a single differential equation for dp/dz in terms of p and z.
 
Last edited by a moderator:

FAQ: Calculate the pressure at this altitude?

1. What is the formula for calculating pressure at a given altitude?

The formula for calculating pressure at a given altitude is P = P₀ * e^(-Mgh/RT), where P₀ is the pressure at sea level, M is the molar mass of air, g is the acceleration due to gravity, h is the altitude, R is the universal gas constant, and T is the temperature.

2. How does pressure change with altitude?

As altitude increases, the pressure decreases. This is because the air molecules are more spread out at higher altitudes, resulting in a lower concentration and thus lower pressure.

3. What units are used to measure pressure at different altitudes?

The most common unit for pressure at different altitudes is millibars (mb) or hectopascals (hPa). However, other units such as inches of mercury (inHg) or atmospheres (atm) may also be used.

4. Can altitude affect human body pressure?

Yes, altitude can affect human body pressure. As altitude increases, the pressure decreases, which can lead to conditions such as altitude sickness. This is because the body needs time to acclimate to the change in pressure and oxygen levels.

5. How accurate is the calculation of pressure at a given altitude?

The calculation of pressure at a given altitude can be quite accurate, as long as the necessary variables (such as temperature and molar mass) are accurately measured and the formula is applied correctly. However, there may be some variations due to factors like weather conditions and local topography.

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