A motor tube is filled with air at 27^{circ}C | vedclass

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(C) When a tube bursts suddenly,the process is adiabatic because there is no time for heat exchange with the surroundings.For an adiabatic process,the

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$150 	ext{ K}$

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(C) When a tube bursts suddenly,the process is adiabatic because there is no time for heat exchange with the surroundings.For an adiabatic process,the relationship between temperature and pressure is given by: $T_2 / T_1 = (P_2 / P_1)^{(\gamma - 1) / \gamma}$.Given: Initial temperature $T_1 = 27^{\circ}C = 300 	ext{ K}$,Initial pressure $P_1 = 8 	ext{ atm}$,Final pressure $P_2 = 1 	ext{ atm}$ (atmospheric pressure),and $\gamma = 1.5$.Substituting the values: $T_2 / 300 = (1 / 8)^{(1.5 - 1) / 1.5}$.$T_2 / 300 = (1 / 8)^{0.5 / 1.5} = (1 / 8)^{1/3}$.Since $8^{1/3} = 2$,we have $T_2 / 300 = 1 / 2$.Therefore,$T_2 = 300 / 2 = 150 	ext{ K}$.

$A$ motor tube is filled with air at $27^{\circ}C$ and a pressure of $8 \text{ atm}$. If the tube suddenly bursts,what will be the final temperature of the air? $(\gamma = 1.5)$

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