Question

magine a giant dry-cleaner’s bag full of air at a temperature of −35°C floating like a balloon with a string hanging from it 10 km above the ground. Estimate what its temperature would be if you were able to yank it suddenly back to Earth’s surface.

Answer 1

The combined gas law states that
P V / T = a constant
If the volume constant then P / T = a constant
Where P and T are pressure and the temperature of the gas at a time
The pressure at 10 km above the sea level is P₁  = 265 milli bar = 26.5 k Pa
The pressure at the sea level is P₂ = 1000 milli bar = 100 k Pa
The temperature of the air at 10 km is T₁   = 238 K
We need to find the temperature at the sea level T₂
Using the above law
P₁ / T₁   = P₂ / T₂
T₂  = (P₂ / P₁) T₁
T₂ = (100 k Pa / 26.5 ) x 238
T₂  = 898.11 K = 625.11⁰C