A spherical air bubble is rising from the depth of a lake when pressure is Patm and temperature is TK. The percentage increase in the radius when it comes to the surface of a lake will be (Assume temperature and pressure at the surface to be, respectively, 2TK and `P"/"4`).

Options

A. `100 %`
B. `50%`
C. `40%`
D. `200%`

Answer

A

Explanation

`(P_(1)V_(1))/(T_1)= (P_(2)V_(2))/(T_2), [(V_(1)-" initial "),(V_(2)-" final volume")]`
`(PV_(1))/(T)= (P)/(4)xx(V_2)/(2T) implies V_(1)= (V_2)/(8) implies V_(2)= 8V_(1)`
`(V_2)/(V_1)= 8 =((r_2)/(r_1))^(3) implies r_(2)= 2r_(1)`.