Question

It is common to see bubbles in fish tank. These bubbles increase in size when they rise from the bottom of the tank to the top. An air bubble at the bottom of a fish tank containing water has volume of 1.0 mm3 . The height of the tank is 1.00m. what is the volume when it rises to the top? Density of water 1000 kg m-3 ; atmospheric pressure : 1.0 × 105 pa; acceleration due to gravity :10

Answer 1

We believe that the temperature remains constant. That's why

$$p_1 V_1 = p_2 V_2 \gg (p + \rho g h) V_1 = V_2 p \gg V_2 = \frac{(p + \rho g h) V_1}{p} = \frac{(1.0 \times 10^5 + 1000 \times 10 \times 1)}{1.0 \times 10^5} \cdot 1.0 \, \mathrm{mm}^3 = 1.1 \, \mathrm{mm}^3$$