Air is filled in a bottle at atmospheric pres | vedclass

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(C) According to the ideal gas law,$PV = nRT$. Since the volume $V$ and the amount of gas $n$ remain constant,we have $P \propto T$,which implies $\fr

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$651$

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(C) According to the ideal gas law,$PV = nRT$. Since the volume $V$ and the amount of gas $n$ remain constant,we have $P \propto T$,which implies $\frac{P_1}{T_1} = \frac{P_2}{T_2}$.Given:Initial pressure $P_1 = 1 	ext{ atm}$Initial temperature $T_1 = 35 + 273 = 308 	ext{ K}$Final pressure $P_2 = 3 	ext{ atm}$Final temperature $T_2 = ?$Substituting the values into the relation:$\frac{1}{308} = \frac{3}{T_2}$Solving for $T_2$:$T_2 = 3 	imes 308 = 924 	ext{ K}$Converting the temperature back to Celsius:$T_2(^{\circ}C) = 924 - 273 = 651^{\circ}C$.

Air is filled in a bottle at atmospheric pressure and it is corked at $35^{\circ}C$. If the cork can come out at $3$ atmospheric pressure,then up to what temperature should the bottle be heated in order to remove the cork? (in $^{\circ}C$)

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