Answer:
B) THE DEPTH OF THE LAKE IS 0.060 m
Explanation:
b) Determine the depth of the lake in metres
1. Using the general gas law, we will calculate the initial pressure of the air bubbles.
P1V1 /T1 = P2V2/T2
P1 = Unknown
T1 = 5.24 °C
T2 = 18.73 °C
P2 = 0.973 atm
V1 = V1
V2 = 6V1
P1 = P2 V2 T1 / V1 T2
P1 = 0.973 * 6V1 * 5.24 / V1 * 18.73
P1 = 5.09852 * 6 / 18.73
P1 = 30.59112 / 18.73
P1 = 1.633 atm.
2. Calculate the depth of the lake:
Pressure = length * density * acceleration
length = Pressure / density * acceleration
Pressure = 1.633 atm = 1.633 * 101, 325 Nm^2 = 165, 463.725 Nm^2
Density = 1.02 g/cm3 = 1.02 * 10^3 kg/m^3
Acceleration = 9.8 m/s^2
So therefore, the length in metres is:
Length = density * acceleration / pressure
Length = 1.02 *10^3 * 9.8 / 165, 463.725
Length = 9.996 * 10^3 / 165 463.725
Length = 0.06 m
Hence, the depth of the lake is 0.06 m
