The question states that 1 atmosphere of pressure, 101,000 Pa, is already present. In order to achieve 2 atmospheres of pressure, we need increase our pressure by another 101,000 Pa. That can be done by descending 10.3 meters down into the lake.
In order to know what the pressure at a given depth within a fluid is, you can use the formula P = dgh
P = pressure
d = density
g = gravity (9.8 m/s/s)
h = depth in the fluid (measured in meters)
Water has a density of 1,000 kg/m^3. From here, we just plug in the numbers and solve for h.
101,000 = 1,000(9.8)h
101,000 = 9,800h
10.3 meters = h
Use the same formula and switch the density to that of mercury (13,600 kg/m^3) to calculate the depth needed to descend to in mercury in order to achieve an additional atmosphere of pressure.
101,000 = 13,600(9.8)h
101,000 = 133,280h
.76 meters = h
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