Answer to Question #242563 in Physics for rubia

Question

An air bubble rises from the bottom of a well where the temperature is 25 0 C, to the surface where the

temperature is 27 0 C. Find the percent increase in the volume of the bubble if the depth of the well is

5m. Atmospheric pressure is 101.528 kPaa.

Answer 1

Use the combined gas law:

$$\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2},\\\space\\ \epsilon=\frac{V_2}{V_1}-1=\frac{T_2P_1}{T_1P_2}-1=\\\space\\=\frac{(27+273)(p_0+\rho gd)}{(25+273)(p_0)}-1=0.007,$$

or 0.7%.