Question 5 of 190

There are two vessels filled with an ideal gas where volume of one is double the volume of other. The large vessel contains the gas at 8 kPa at 1000 K while the smaller vessel contains the gas at 7 kPa at 500 K. If the vessels are connected to each other by a thin tube allowing the gas to flow and the temperature of both vessels is maintained at 600 K , at steady state the pressure in the vessels will be (in kPa).

A$4.4$B$6$C$24$D$18$

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Answer: (B) $6$

Number of masses will remain constant
$\begin{aligned}
& \mathrm{n}_1+\mathrm{n}_2=\mathrm{n}_{\mathrm{f}} \\
& \frac{\mathrm{P}_1 \mathrm{~V}_1}{\mathrm{RT}_1}+\frac{\mathrm{P}_2 \mathrm{~V}_2}{\mathrm{RT}_2}=\frac{\mathrm{P}_{\mathrm{f}} \mathrm{~V}_{\mathrm{f}}}{\mathrm{RT}_{\mathrm{f}}} \\
& \frac{8 \times 2 \mathrm{~V}}{\mathrm{R} \times 1000}+\frac{7 \times \mathrm{V}}{\mathrm{R} \times 500}=\frac{\mathrm{P}_{\mathrm{f}}(3 \mathrm{~V})}{\mathrm{R} \times 600} \\
& \frac{16}{1000}+\frac{14}{1000}=\frac{\mathrm{P}_{\mathrm{f}}}{\mathrm{R} \times 600} \\
& \frac{30}{1000}=\frac{\mathrm{P}_{\mathrm{f}}}{200} \\
& \mathrm{P}_{\mathrm{f}}=6 \mathrm{kPa}
\end{aligned}$