At 27^∘ C, a motor car tyre has a pressure of 2 atmospheres....

At $27^{\circ} \mathrm{C}$, a motor car tyre has a pressure of 2 atmospheres. The temperature, if the tyre suddenly burst will be : (Given: $\gamma_{\text {air }}=1.4$ )
(a) $246.1 \mathrm{~K}$
(b) $250 \mathrm{~K}$
(c) $246.1^{\circ} \mathrm{C}$
(d) $248 \mathrm{~K}$

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Key Concepts

Poisson's Equations

Poisson's equations relate the pressure, volume, and temperature of an ideal gas undergoing an adiabatic process. Specifically, the relationship T2/T1 = (P2/P1)^((? - 1)/?) is used to calculate the new temperature after a sudden change in pressure. This mathematical relationship is essential for predicting the temperature evolution in adiabatic expansions or compressions, given the specific heat ratio (?) of the gas.

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 is compressed adiabatically, its internal energy changes solely due to work done, which in turn influences the temperature of the gas. This concept is crucial in understanding rapid processes where heat transfer is negligible compared to the work done, such as in a bursting tyre.

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