Answer
$W = 2.453\times10^{-6} \ BTU$
Work Step by Step
The equation for the work is:
$W = \int \gamma dA$
Since we're expanding both the inner and outer walls (with assumed negligible thickness):
$W = \int 2\gamma dA$
Therfore:
$W = 2\gamma \times(A_{final}-A_{initial})$
$A_{sphere} = \pi D^2$
$W = 2\pi\gamma \times(D^2_{final}-D^2_{initial})$
With:
$\gamma = 0.005 lbf/ft$
$D_{initial} = 0.5 in \times \frac{1 \ in}{12 \ ft} = 0.04167 ft$
$D_{final} = 3.0 in \times \frac{1 \ in}{12 \ ft} = 0.25 ft$
$W = 1.909\times10^{-3} \ lbf.ft \times \frac{1\ BTU}{778.2\ lbf.ft}$
$W = 2.453\times10^{-6} \ BTU$
