An air bubble starts rising from the bottom of a lake. Its diameter is 3.6 mm at the bottom and 4 mm at the surface. The depth of the lake is 2.5 m and the temperature at the surface is 40^(@)C. What is the temperatue at the bottom of the lake ?

An air bubble starts rising from the bottom of a lake. Its diameter is

1.	An air bubble starts rising from the bottom of a lake. Its diameter is 3.6 mm at the bottom and 4 mm at the surface. The depth of the lake is 2.5 m and the temperature at the surface is 40^(@)C. What is the temperatue at the bottom of the lake ?
Answer» SOLUTION :Let `P_(1), V_(1), T_(1)" and "P_(2), V_(2), T_(2)` are the parameters of the air bubble at the bottom and surface of the lake respectively. `P_(1)=` ATM/PRESSURE + Pressure of water at the bottom `""=(76 times 13.6 times 980)+(250 times 1 times 980)=1283.6 times 980" dyne "cm^(-2)` `P_(2)="Atm. pressure"=76 times 13.6 times 980=1033.6 times 980" dyne "cm^(-2)` `V_(1)=4/3pi(0.36/2)^(3)=0.007776 times PI cm^(3) rArr V_(2)=4/3pi(0.4/2)^(3)=0.01067 times picm^(3)` `T_(2)=273+40=313K` From the equation, `(P_(1)V_(1))/T_(1)=(P_(2)V_(2))/T_(2)` `rArr T_(1)=P_(1)/P_(2) times V_(1)/V_(2) times T_(2)=(1283.6 times 980)/(1033.6 times 980) times (0.00776pi)/(0.01067pi) times 313=1.242 times 0.7288 times 313=283.3K` Temperature at the bottom of the lake = 283.3 - 273 = `10.3^(@)C`