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(A) Initially,the number of moles of gas in each bulb is $n_1 = \frac{P_i V}{R T_1}$ and $n_2 = \frac{P_i V}{R T_1}$.After the temperature of the seco

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$2 P_i \left( \frac{T_2}{T_1 + T_2} \right)$

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(A) Initially,the number of moles of gas in each bulb is $n_1 = \frac{P_i V}{R T_1}$ and $n_2 = \frac{P_i V}{R T_1}$.After the temperature of the second bulb is raised to $T_2$,the number of moles of gas in both bulbs are $n_1' = \frac{P_f V}{R T_1}$ and $n_2' = \frac{P_f V}{R T_2}$.Since the total number of moles of gas in both bulbs remains constant:$n_1 + n_2 = n_1' + n_2'$$\frac{P_i V}{R T_1} + \frac{P_i V}{R T_1} = \frac{P_f V}{R T_1} + \frac{P_f V}{R T_2}$$\frac{2 P_i V}{R T_1} = \frac{P_f V}{R} \left( \frac{1}{T_1} + \frac{1}{T_2} \right)$$\frac{2 P_i}{T_1} = P_f \left( \frac{T_2 + T_1}{T_1 T_2} \right)$$P_f = \frac{2 P_i T_2}{T_1 + T_2}$

Two closed bulbs of equal volume $V$ containing an ideal gas initially at pressure $P_i$ and temperature $T_1$ are connected through a narrow tube of negligible volume as shown in the figure below. The temperature of one of the bulbs is then raised to $T_2$. The final pressure $P_f$ is:

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