A motor-car tyre has a pressure of 2, atm at | vedclass

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(C) sudden burst of a tyre is an adiabatic process because the change happens very quickly,allowing no time for heat exchange with the surroundings.Fo

Vedclass · Accepted Answer

$-27\,^{\circ}C$

Vedclass · Answer

(C) sudden burst of a tyre is an adiabatic process because the change 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 $T^{\gamma} P^{1-\gamma} = 	ext{constant}$,or $T P^{(1-\gamma)/\gamma} = 	ext{constant}$.Initial state: $T_1 = 27 + 273 = 300\, K$,$P_1 = 2\, atm$.Final state: $P_2 = 1\, atm$ (atmospheric pressure),$T_2 = ?$.Using the relation $T_1 P_1^{(1-\gamma)/\gamma} = T_2 P_2^{(1-\gamma)/\gamma}$:$T_2 = T_1 \left( \frac{P_1}{P_2} ight)^{(1-\gamma)/\gamma} = 300 \left( \frac{2}{1} ight)^{(1-1.4)/1.4} = 300 	imes (2)^{-0.4/1.4} = 300 	imes (2)^{-2/7} = 300 	imes (4)^{-1/7}$.Given $4^{1/7} = 1.219$,so $T_2 = \frac{300}{1.219} \approx 246\, K$.Converting to Celsius: $T_2 = 246 - 273 = -27\,^{\circ}C$.

$A$ motor-car tyre has a pressure of $2\, atm$ at $27\,^{\circ}C$. It suddenly bursts. If $\gamma = \frac{C_p}{C_v} = 1.4$ for air,find the resulting temperature. (Given $4^{1/7} = 1.219$)

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