Volume Expansion Calculation: 0.81632 cm^3

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Homework Statement

At 19 m below the surface of the sea (den-
sity of 542 kg/m^3), where the temperature is
7 degree C, a diver exhales an air bubble having a
volume of 0.8 cm^3.
If the surface temperature of the sea is 13 degree C,
what is the volume of the bubble immediately
before it breaks the surface? The acceleration
of gravity is 9.8 m/s^3 and the atmospheric
pressure is 1.02 × 105 Pa. Answer in units of
cm^3.

Homework Equations

$$\Delta$$V = $$\beta$$Vinitial$$\Delta$$T

The Attempt at a Solution

Vfinal - Vinitial = $$\beta$$Vinitial(Tfinal - Tinitial)
Vfinal = $$\beta$$Vinital(Tfinal - Tinitial) + Vinitial
= (3400x10^-6)(0.8)(13-7) + 0.8
= 0.81632 cm^3

 

[Doc Al]

Rather than attempt to use a volume expansion formula (which might only apply under certain conditions, such as constant pressure), consider the basic properties of a gas. How are pressure, volume, and temperature of a gas related?