Answer to Question #83935 in Molecular Physics | Thermodynamics for Tran Thi Tuyet Mai

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 Clausius-Clapeyron equation states

pV=nRT

So,

(p_1 V_1)/T_1 =(p_2 V_2)/T_2

Thus

V_2/V_1 =p_1/p_2 ×T_2/T_1 =3.50/1.00×(4.0+19.0+273)/(4.0+273)=3.74 times