A ball of volume V=8 L is full of air with pressure higher than atmospheric pressure by Δp=2×10^4 Pa. The total mass of the ball and the air inside is 200 g. The ball is tossed up to a height h=20 m, then it falls down, collides with the ground, and bounces back up. Estimate the highest temperature the air inside the ball could reach during the collision in Celsius.

Details and assumptions
The gravitational acceleration is g=−9.8 m/s^2.
The atmospheric pressure is po=10^5 Pa.
The specific heat of air is C=700 J/kgK.
The temperature of the surrounding environment is To=27∘C.
The mass per mol of air is μ=29 g/mol.
The gas constant is R=8.31 J/molK.
Treat air as an ideal gas to simplify the problem.
Neglect air resistance.