Answer to Question #84010 in Molecular Physics | Thermodynamics for Diệp Thùy Linh

Question

A diver observes a bubble of air rising from the bottom of a lake (where the absolute pressure is 3.50 atm) to the
surface (where the pressure is 1.00 atm). The temperature at the bottom is 4.0°C, and the temperature at the surface is
19.0C° higher. Find the ratio of the volume of the bubble as it reaches the surface to its volume at the bottom? Does
the bubble expand or compress in volume? Assume that the number of moles of gas in the bubble remains constant

Answer 1

The equation of states for ideal gas gives

P_1 V_1=nRT_1

P_2 V_2=nRT_2

So

V_2/V_1 =(P_1 T_2)/(P_2 T_1 )

=(3.50 atm×277K)/(1.00 atm×292K)

=3.32

Therefore, the bubble expands in volume by 3.32 times.