What will happen to the volume of a bubble of air found under water in a lake, where the temperature is `15^(@)C` and the pressure is 1.5 atm. If the bubble then rises to the surface where the temperature is `25^(@)C` and the pressure is 1.0 atm ?

Options

A. Its volume will become greater by a factor of 2.5
B. Its volume will become greater by a factor of 1.6
C. Its volume will become greater by a factor of 1.1
D. Its volume will become greater by a factor of 0.70

Answer

B

Explanation

`(p_(1)V_(1))/( T_(1)) = ( p _(2) V_(2))/( T_(2))`
`p_(1) = 1.5 atm, T_(1) = 273 + 15 = 288 K `
`p_(2) = 1.0 atm, T_(2) = 273 + 25 = 298 K`
`( 1.5 xx V_(1)) /( 288) = ( 1 xx V_(2))/( 298)`
`V_(2) = ( 1.5 xx V_(1) xx 298)/(288 xx 1 )`
`1.55 V_(1) = 1.6 V_(1)`