Question

Air (γ = 1.4) is pumped at 2 atm pressure in a motor tyre at 20°C. If the tyre suddenly bursts, what would be the temperature of the air coming out of the tyre? Neglect any mixing with the atmospheric air.

Answer 1

Given:
For air, γ = 1.4
Initial temperature of air, T₁ = 20°C = 293 K
Initial pressure, P₁ = 2 atm
Final pressure, P₂ = 1 atm
The bursting of the tyre is an adiabatic process. For an adiabatic process,

P₁^1−γ × T₁^1−γ = P^1−γ × T₂^γ
(2)^1−1.4 × (293)^1.4 = (1)^1−1.4 × T₂^1.4
⇒ (2)^−0.4 × (293)^1.4 = T₂^1.4
⇒ 2153.78 = T₂^1.4
⇒ T₂ = (2153.78)^1/1.4
= 240.3 K