When water boils, small bubbles form at the bottom and get larger as they rise.

Question

When water boils, small bubbles form
at the bottom and get larger as they rise. Bubbles get larger due to the decreasing
pressure exerted on them by the water as
they rise. The absolute pressure on the bubble
is predicted by the hydrostatic equation : p = 2116 ? 62.4(h)
where 62.4 lbm/ft^3 is the density of water and
h is the depth of the bubble from the top water
level. The expansion of the bubble as it is rising
is a constant temperature process.

a) If water is boiling in a 10-ft deep vessel at
212?F, what is the volume occupied (ft^3) of a
bubble that contains .0001 lb of steam?

b) How big (volume) does the bubble get
when it reaches the top? (Remember that the
expansion is a constant temperature thermodynamic
process)

c) How much WORK is done by the bubble
as it expands?

Explanation / Answer

ans)

a)

Pl note there may be discrepancy in the pressure equation(P=2116-62.4h) as the pressure should reduce as h reduces, but here it increases with reduced h. So we assume the equation as

P=2116+62.4h to look more consistent

Hence P at 10 ft depth

P=2116+10x62.4 = 2740 psf = 19.03 psi

At 19.03 psia the saturated steam specific volume is

v=0.0168 ft3/lbm

Hence volume of 0.0001lb bubble

V=0.0001x0.0168

=1.68x10-6 ft3

V=1.68x10-6 ft3

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