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?

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- Jul 31st 2006, 04:31 PMCeliaA 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 PMtopsquarkQuote:

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