Two closed vessels of same volume are joined through a narrow tube and both vessels are filled with air of pressure 90 kPa and temperature 400 K

Question

Two closed vessels of same volume are joined through a narrow tube and both vessels are filled with air of pressure 90 kPa and temperature 400 K. Keeping the temperature of one vessel constant at 400 K, the second vessel temperature is raised to 500 K. The final pressure in the vessels is ______ kPa. [2026]

Smart Achievers · Accepted Answer

(1)

$Using mole conservation: n_{total} = n_{1} + n_{2}$

$\frac{P_{f} V}{T_{f}} + \frac{P_{f} V}{T_{f}} = \frac{P_{i} V}{T_{i}} + \frac{P_{i} V}{T_{i}}$

$P_{f} V (\frac{1}{400} + \frac{1}{500}) = \frac{2 P_{i} V}{T_{i}}$

$P_{f} \times V \times \frac{900}{400 \times 500} = \frac{2 \times 90 \times 10^{3} \times V}{400}$

$P_{f} = \frac{180 \times 10^{3} \times 5}{9} = 180 \times 10^{3} Pa = 100 kPa$

Solution

1 100

2 120

3 90

4 105

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