A driver releases an air bubble of volume 2.0 cm3 from a depth of 15 m below the surface of a lake, where the temperature is 7.0oC. What is the volume of the bubble when it reaches just below the surface of the lake, where the temperature is 20oC?
A driver releases an air bubble of volume 2.0 cm3 from a depth of 15 m below the surface of a lake, where the temperature is 7.0oC. What is the volume of the bubble when it reaches just below the surface of the lake, where the temperature is 20oC?
BIG warning on this one: Watch your units!Originally Posted by Celia
Assume that air is an ideal gas (not too bad an approximation.)
We need pressures. 15 m below the surface of the water $\displaystyle P_1 = P_0 + \rho g (15 \, m)$ and P2 = P0 (at the surface), where P0 = 1.01 x 10^5 Pa. (I'm going to presume we can take $\displaystyle \rho = 1 \, g/cm^3 = 1000 \, kg/m^3$.) Thus P1 = 157100 Pa.
V1 = 2.0 cm^3 = 2.0 x 10^(-6) m^3.
Finally, T1 = 273 K + 7 K = 280 K and T2 = 273 K + 20 K = 293 K.
$\displaystyle \frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}$
$\displaystyle V_2 = \frac{P_1V_1}{T_1} \cdot \frac{T_2}{P_2}$
I get V2 = 32.553 x 10^(-6) m^3 = 33 cm^3.
-Dan