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(D) Let the volume of each bulb be $V$. Initially,both bulbs are at $T_1 = 273 \ K$ and pressure $P$. The total number of moles $n$ is given by:$n = \

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$546$

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(D) Let the volume of each bulb be $V$. Initially,both bulbs are at $T_1 = 273 \ K$ and pressure $P$. The total number of moles $n$ is given by:$n = \frac{PV}{RT_1} + \frac{PV}{RT_1} = \frac{2PV}{RT_1}$When one bulb is at $T_1 = 273 \ K$ and the other is at $T_2$,the new pressure is $P' = 1.5P$. The total number of moles remains constant:$n = \frac{P'V}{RT_1} + \frac{P'V}{RT_2} = \frac{1.5PV}{RT_1} + \frac{1.5PV}{RT_2}$Equating the two expressions for $n$:$\frac{2PV}{RT_1} = \frac{1.5PV}{RT_1} + \frac{1.5PV}{RT_2}$$\frac{2}{273} = \frac{1.5}{273} + \frac{1.5}{T_2}$$\frac{0.5}{273} = \frac{1.5}{T_2}$$T_2 = 273 	imes \frac{1.5}{0.5} = 273 	imes 3 = 819 \ K$Converting to Celsius: $T_2(^{\circ}C) = 819 - 273 = 546^{\circ}C$.

Two identical glass bulbs are connected by a thin glass tube. The system is filled with gas at $0^{\circ}C$. If one bulb is placed in ice and the other in hot water,the pressure of the gas becomes $1.5$ times the initial pressure. What is the temperature of the hot water in $^{\circ}C$?

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