Question

It is a hot, sunny day. The outdoor temperature is 32°c (90°f), and the water temperature is 21°c (70°f). A scuba diver submerses himself while holding a balloon filled with 1.5 l of air. If the balloon shrinks to a volume of 0.5 l at a depth of 20 m, what is the pressure at this depth? (assume that the outdoor pressure is 1 atm.)

Answer 1

initially when balloon is in atmosphere then we have

`PV = nRT`

initial temperature is T = 32 degree C

Initial pressure P = 1 atm

Initial volume V = 1.5 L

now we have number of moles as

`n = (1*1.5)/(R*(32 + 273))</p><p>similarly when it is submerged into the water</p><p>Temperature will be T = 21 degree C</p><p>Volume will be 0.5 L</p><p>now for same number of moles</p><p>[tex]PV = nRT`

`P*0.5 = (1*1.5)/(R * 305)* R* (21+273)`

`P = 2.89 atm`

so pressure at this depth will be 2.89 atm