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Question

A bulb of constant volume is attached to a manometer tube open at other end as shown in the figure. The manometer is filled with a liquid of density (1/3)rd that of mercury. Initially h was 228cm. Through a small hole in the bulb, gas leaked. Assuming the pressure decreases as dPdt=kP and the value of h is 114cm after 14min. What is the value of k (in hour1)? (ln(4/3)=0.28 and density of Hg=13.6g/mL)
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A
0.6
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B
1.2
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C
2.4
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D
none of the above
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Solution

The correct option is C 1.2
P=P0ekt;P0=2283+76=152cmHg
At t=14min;P=1143+76=114cmHg
152ekt=114
k=1tln152114=114×0.28
=0.02×60hr1=1.2hr1

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