Calculating Adiabatic Cooling at 1000 Meters Using Atmospheric Law

[EzequielSeattle]

Homework Statement

A pocket of air rises 1000 meters. Estimate how much it cools. Use the atmospheric law to determine pressure at 1000 meters.

Homework Equations

P = P₀ * e^-Mgz/RT
PV^γ = constant
TV^γ-1 = constant

The Attempt at a Solution

Using the atmospheric law, I found the pressure at 1000 meters to be 90202 Pa, or about 0.89 atm. I'm not sure how to use the adiabatic equations. I just assumed V₁ was 1 m³, and also assumed that γ=(5/7), as the atmosphere is mainly diatomic. Plugging these in, I got that the gas expands to about 1.09 m³, but when I tried to plug that into my last equation, I got that the gas actually HEATS up, which I know is wrong. What did I do wrong? Please help!

 

[Quantum Defect]

Homework Statement

A pocket of air rises 1000 meters. Estimate how much it cools. Use the atmospheric law to determine pressure at 1000 meters.

Homework Equations

P = P₀ * e^-Mgz/RT
PV^γ = constant
TV^γ-1 = constant

The Attempt at a Solution

Using the atmospheric law, I found the pressure at 1000 meters to be 90202 Pa, or about 0.89 atm. I'm not sure how to use the adiabatic equations. I just assumed V₁ was 1 m³, and also assumed that γ=(5/7), as the atmosphere is mainly diatomic. Plugging these in, I got that the gas expands to about 1.09 m³, but when I tried to plug that into my last equation, I got that the gas actually HEATS up, which I know is wrong. What did I do wrong? Please help!

What is gamma? it should be the ratio of Cp/Cv, correct? Which is larger, Cp or Cv ? Should gamma be greater or less than one?

 

[EzequielSeattle]

Thank you! I was accidentally using γ=5/7 instead of 7/5. It works now.