Answer
$(d) 140 h$
Work Step by Step
For an isothermal process, T is constant, so
$\frac{V_2}{V_1} = \frac{p_1}{p_2}$
$V_2 = V_1 \frac{p_1}{p_2}$
$V_2 = (500 L) \frac{2014.7 psi}{14.7 psi}$
$V_2 = 68527 L$
The volume of gas lost
$V = V_2 - V_1 $
$V = 68527 L - 500 L $
$V = 6.8 \times 10^4 L$
Now the rate is $R = \frac{V}{t}$ Solve for t
$t = \frac{V}{R}$
$t = \frac{6.8 \times 10^4 L}{8.2 L/min}$
$t = 8.3 \times 10^3 min = 138.3 h $
The closest answer is choice $(d) 140 h$
