A bulb of constant volume is attached to a manometer tube open at other end as shown in figure. The manometer is filled with a liquid of density `(1//3)^("rd")` that of mercury. Initially h was 228 cm.

Through a small hole in the bulb gas leaked assuming pressure decreases as `(dP)/(dt)=-kp.`If value of h is 114 cm after 14 minutes, what is the value of k (in `"hour"^(-1)`)?
[ Use : In (4/3) =0.28 and density of Hg =13.6 g/mL.].

Options

A. 0.6
B. 1.2
C. 2.4
D. none of these

Answer

b

Explanation

(b) `P=P_(0^(e^(-kt))),P_(0)=(228)/(3)+76=152cm Hg`
`"At "t=14 min,P=(114)/(3)+76=114cm Hg`
`implies" "152e^(-kt)=114`
`impliesk=(1)/(t)"In"(152)/(114)=(1)/(14)xx0.28`
`=0.02xx60hr^(-1)=1.2hr^(-1)`