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One summer, while working as a lifeguard at a summer camp, a coworkers had the i

ID: 1852572 • Letter: O

Question

One summer, while working as a lifeguard at a summer camp, a coworkers had the idea to create what he called the "underwater cabana." It consisted of a canoe anchored upside down to the bottom of the lake and filled with air. He thought it would be a fun place to hang out on our breaks. Assume a canoe which holds a maximum volume (Vcanoe) submerged and anchored in a lake of known temperature (Tlake). If the goal was to fill the canoe half full of air, such that the air-water interface (ie. the dashed line) was a distance z below the surface of the lake, what is the mass of air (mair) needed? Express your answer in terms of the variables given and any constants needed. Solve for the mass of air needed if Vcanoe = 0.5 m3, Tlake = 10 degree C, z = 1 m.

Explanation / Answer

PV=mRT
P=Pa+gh T=temperature of air in kelvin ;V=0.5*Vmax m=mass of air; R=specific gas constant(air)=286.9J/K kg (this is not the universal gas constant)

h=z depth of immersion; =density of water

a)m=PV/RT

b)m=(101325+1000*9.8*1)((0.5*)*0.5)/(286.9*273+10)=5.0401 kg