Question

An air bubble starts rising from the bottom of a lake. Its diameter is 3.6 mm at the bottom and 4 mm at the surface. The depth of the lake is 250 cm and the temperature at surface is 40°C. What is the temperature at the bottom of the lake? Given atmospheric pressure = 76 cm of Hg and $g = 980 \, \text{cm/s^2$}

• A. 11°C
• B. 12.36°C
• C. 13°C
• D. 10.37°C

Hint:

Remember that changes in pressure at greater depths affect the volume and temperature of the air bubble.

Answer 1

The Correct Option is D

Using the ideal gas law, we know that temperature and volume are related by: \[ P V = \frac{n R T}{P} \] Since the pressure at the bottom of the lake is higher than at the surface, this causes the volume of the bubble to change. We can use this to find the temperature at the bottom, which is found to be $10.37^\circ$C.