# A driver.....

• Jul 31st 2006, 04:31 PM
Celia
A driver.....
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?
• Jul 31st 2006, 04:49 PM
topsquark
Quote:

Originally Posted by Celia
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!

Assume that air is an ideal gas (not too bad an approximation.)

We need pressures. 15 m below the surface of the water $P_1 = P_0 + \rho g (15 \, m)$ and P2 = P0 (at the surface), where P0 = 1.01 x 10^5 Pa. (I'm going to presume we can take $\rho = 1 \, g/cm^3 = 1000 \, kg/m^3$.) 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.

$\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}$

$V_2 = \frac{P_1V_1}{T_1} \cdot \frac{T_2}{P_2}$

I get V2 = 32.553 x 10^(-6) m^3 = 33 cm^3.

-Dan