Question

A small bubble rises from the bottom of a lake, where the temperature and pressure are 6C and 3.0 atm, to the water's surface, where the temperature is 25C and the pressure is 0.75 atm. Calculate the final volume of the bubble if its initial volume was 3.1 mL

Answer 1

SOLUTION: To find the final volume of a bubble when it rises from the bottom of a lake to the waters surface GIVEN: 1) When bubble is at the bottom of lake Temperature (T.) = 66 +273 =1279 Pi = 3:0 atm Initial volume (V.)=3,1 mL. To convert volume from mL to L (litre). TL = 1000mL. :. x L = 3.1 mL implies & 1X3.1 = xx1000 = x=3.1 3.1810 L 1000 2) When bubble is at water's surface Iz = 25°c +273 = 1298k) ; [P2=0.75 atm! V2 = ? Using the relation, PV=RT. At I → Piv,ERT, PV =R At e Pa = RT2 P2 Va a R.T . Te Since RHS of equation and 6 are same 'we can equate LHS of these equations PV = P₂ V₂ Ti Te (3.0) (BelX603) - 10.75) (2), (279) (298)

3333 X105(2,514 x 10-2)(vw). . V2 = 3.333 x 10-5 2:517x1013 a. Va = 0.0132 L or va = 13.2 mL he final volume of the bubble will be 113.2 mL
The given problem can be easily solved by using ideal gas equation for one mole and taking all the units in the MKS system.