Question

An air bubble has a volume of 1.1 cm3 when it is released by a submarine 110 m below the surface of a freshwater lake. What is the volume of the bubble (in cm3) when it reaches the surface? Assume that the temperature and the number of air molecules in the bubble remain constant during the ascent. (The density of water is 1,000 kg/m3.)

Answer 1

`V = 12.85 cm^3`

Step-by-step explanation:

As we know that initially the air bubble is at depth 110 m

so the pressure of the air bubble is given as

`P = P_o + \rho gh`

`P = 1.01 * 10^5 + (1000)(9.81)(110)`

`P = 1.18 * 10^6 Pa`

initial volume of the bubble is given as

`V = 1.1 cm^3`

now we know that here temperature of air bubble is constant

so we have

`P_1 V_1 = P_2 V_2`

`(1.18 * 10^6)(1.1 cm^3) = (1.01 * 10^5) V`

`V = 12.85 cm^3`