The pressure in the tyre of a car is four tim | vedclass

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(D) sudden bursting of a tyre is an adiabatic process because the expansion happens very quickly,allowing no time for heat exchange with the surroundi

Vedclass · Accepted Answer

$300 \ (4)^{-0.4/1.4}$

Vedclass · Answer

(D) sudden bursting of a tyre is an adiabatic process because the expansion happens very quickly,allowing no time for heat exchange with the surroundings.For an adiabatic process,the relationship between temperature $T$ and pressure $P$ is given by $T^\gamma P^{1-\gamma} = 	ext{constant}$.This can be written as $T_1^\gamma P_1^{1-\gamma} = T_2^\gamma P_2^{1-\gamma}$.Rearranging for $T_2$,we get $\frac{T_2}{T_1} = \left( \frac{P_1}{P_2} ight)^{\frac{1-\gamma}{\gamma}}$.Given: $T_1 = 300 \ K$,$P_1 = 4P_{atm}$,$P_2 = P_{atm}$,and $\gamma = 1.4$.Substituting the values: $\frac{T_2}{300} = \left( \frac{4P_{atm}}{P_{atm}} ight)^{\frac{1-1.4}{1.4}}$.$\frac{T_2}{300} = (4)^{\frac{-0.4}{1.4}}$.Therefore,$T_2 = 300 \ (4)^{-0.4/1.4}$.

The pressure in the tyre of a car is four times the atmospheric pressure at $300 \ K$. If this tyre suddenly bursts,its new temperature will be $(\gamma = 1.4)$.

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