Air (γ=1.4) is pumped at 2 atm pressure in a motor tyre at 20^∘ C. If the tyre suddenly bursts,

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Air (γ=1.4) is pumped at 2 atm pressure in a motor tyre at...

Air $(\gamma=1.4)$ is pumped at 2 atm pressure in a motor tyre at $20^{\circ} \mathrm{C}$. 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.

Key Concepts

Irreversible Process

An irreversible process is characterized by a rapid departure from equilibrium, meaning that the system does not undergo a series of quasi-static states. In the context of a sudden tyre burst, the process is irreversible because the gas rapidly expands and the conventional reversible relations lose exact accuracy. However, for practical calculations, it is common to use the reversible adiabatic formulas as approximations in these scenarios.

Ideal Gas

The ideal gas concept assumes that the gas particles do not interact and that their size is negligible, allowing the gas to follow the ideal gas law (PV = nRT) exactly. This simplification is critical when using mathematical relationships to relate pressure, volume, and temperature during processes like adiabatic expansion, and it is commonly assumed in many thermodynamic problems.

Adiabatic Process

An adiabatic process is one in which no heat is exchanged between the system and its surroundings. In thermodynamics, when a gas expands or compresses adiabatically, its change in internal energy is solely due to the work done on or by the system. This concept is fundamental when analyzing rapid processes where there is insufficient time for heat transfer, making it apt for situations like a tyre burst.

Adiabatic Expansion Relation

The adiabatic expansion relation for an ideal gas provides a connection between pressure and temperature, usually expressed as T?/T? = (P?/P?)^((? - 1)/?) for a reversible process. This relation allows one to calculate the change in temperature when a gas expands (or compresses) without exchanging heat with its environment. Even though some rapid processes are irreversible, this relation is often used as an approximation when heat transfer is negligible.

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