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Ideal Gas Equation

Three closed ...

Question

Three closed rigid vessels A, B and C without energy transfer with surroundings, which initially contain three different gases at different temperatures are connected by tube of negligible volume. The vessel A contain 2 mole Ne gas at temperature 300 K, vessel 'B' contains 2 mol of $S O_{2}$ (g) at 400 K and vessel C contains 3 mole of $C O_{2}$ (g) at temperature 500 K. What is the final pressure (in atm) attained by gases when all valves of connecting three vessels are opened and additional 15.6 kcal heat supplied to vessel through valve. The volume of A, B and C vessel is 2, 2 and 3 litre respectively.
Given : $R = 2 c a l o r i e / m o l - K; C_{v} (N e) = 3 / 2 R, C_{v} (C O_{2}) = 5 / 2 R$ and $C_{v} (S O_{2}) = 3 R$

A

73.89 atm

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B

67.31 atm

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C

80 atm

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D

None of these

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Solution

The correct option is A 73.89 atm
heat provided= 15.6 kcal

Total heat recieved by gass = heat provided = $2 \times \frac{3}{2} R (T_{f} - 300) + 2 \times 3 R (T_{f} - 400)$ $+ 3 \times \frac{5}{3} R (T_{f} - 500) = 15600$
$T_{f} = 900 K$
$P_{f} = \frac{900 \times 0.0821 \times 7}{7}$
$P_{f} = 73.89$ atm

Hence, the correct option is $A$

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