Question

Please show work.

40) As shown in the figure, an air pocket atthe top of a vertical tube, closed at the upper end and open at the lower, occupies a volume of 560 cm3 at the surface of a lake where the air pressure is 1.0 x105 Pa and the temperature is 37oC. What is the volume of the air in the pocket if the tube is taken to a depth of 56 meters, where the temperature is 7eC? Assume that none of the air escapes from the tube. The density of the water in the lake is 1000 kg/m3. Air Water

Answer 1

When we are at the surface, we use the ideal gas equation:

when we are at 56 m deper:

so, using these equation and solving for Vf

$V_f = \frac{p_iT_f}{p_fT_i}V_i$

where:

$p_i = p_0 = 1.0\times 10^5 Pa$

$p_f = p_0 +\rho g h = 1.0\times 10^5 +(1000)(9.81)(56) = 6.4936 \times 10^5 Pa$

we calculate Vf