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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.
Solution
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,
P11-γ × T11-γ = P 1-γ × T2γ
(2)1-1.4 × (293)1.4 = (1) 1-1.4 × T21.4
⇒ (2)-0.4 ×(293)1.4 = T21.4
⇒ 2153.78 =T21.4
⇒ T2 =( 2153.78)1/1.4
= 240.3K
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