Calculating Adiabatic Cooling at 1000 Meters Using Atmospheric Law

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A pocket of air rising 1000 meters cools due to adiabatic processes, with the pressure at that altitude calculated to be 90202 Pa or approximately 0.89 atm. The user initially assumed a volume of 1 m³ and used γ=(5/7), leading to incorrect results indicating heating instead of cooling. Upon clarification, it was confirmed that γ should be the ratio of Cp/Cv, which is 7/5 for diatomic gases. Correcting this value resolved the issue, allowing for accurate calculations of cooling. Understanding the correct value of γ is crucial for applying adiabatic equations effectively.
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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
PVγ = constant
TVγ-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!
 
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EzequielSeattle said:

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
PVγ = constant
TVγ-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?
 
Thank you! I was accidentally using γ=5/7 instead of 7/5. It works now.
 
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