Question

An air bubble of `20 cm^3` volume is at the bottom of a lake `40 m` deep where the temperature is `4^@ C`. The bubble rises to the surface which is at a temperature of `20 ^@ C`. Take the temperature to be the same as that of the surrounding water and find its volume just before it reaches the surface.

Answer 1

Correct Answer - A::C
`n_1 = n_2`
`:. (p_1 V_1)/(R T_1) = (p_2 V_2)/(R T_2)`
`:. V_2 = (p_1 V_1 T_2)/(p_2 T_1) = ((p_0 + rho g h)V_1 T_2)/(p_0 T_1)`
= `((1.01 xx 10^5 + 10^3 xx 10 xx 40)(20)(273 +20))/(1.01 xx 10^5 (273 +4)`
=`105 cm^3`.