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

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Solution

Q.
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). [2025]

1 4.4

2 6

3 24

4 18

Ans.
(2)

Number of masses will remain constant

$n_{1} + n_{2} = n_{f}$

$\frac{P_{1} V_{1}}{R T_{1}} + \frac{P_{2} V_{2}}{R T_{2}} = \frac{P_{f} V_{f}}{R T_{f}}$

$\frac{8 \times 2 V}{R \times 1000} + \frac{7 \times V}{R \times 500} = \frac{P_{f} (3 V)}{R \times 600}$

$\frac{16}{1000} + \frac{14}{1000} = \frac{P_{f}}{200}$

$\frac{30}{1000} = \frac{P_{f}}{200} \Rightarrow P_{f} = 6 kPa$

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