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.].

Answer

24

Explanation

`P=P_(@)e^(-kt)`
`P_@=228/3+76=152 cm` Hg
At t=7 min
`P=114/3+76=114` cm Hg
`implies 152 e^(-kt)=114 implies k=1/t "In" 152/114=1/7xx0.28=0.04 min^(-1) =0.04xx60 hr^(-1)=2.4 hr^(-1)`