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In an adiabatic change no heat is exchanged, so PV^gamma stays constant and temperature changes with it: T2/T1 = (V1/V2)^(gamma-1). Compressing air fourfold at gamma = 1.4 raises pressure nearly sevenfold and temperature by 74%. This is why a bicycle pump warms up and why diesel engines ignite without a spark.
Adiabatic relation
P1 V1^gamma = P2 V2^gamma
Temperature
T2 / T1 = (V1 / V2)^(gamma - 1)
1.67 for monatomic gases like helium, 1.4 for diatomic gases like air and nitrogen, and about 1.3 for triatomic gases such as carbon dioxide.
Because all the work done on it goes into internal energy - none escapes as heat, since the process is by definition insulated.