(Solved): Compressed air can be pumped underground into huge caverns as a form of energy storage. The volume ...

Compressed air can be pumped underground into huge caverns as a form of energy storage. The volume of a cavern is \( 4.2 \times 10^{5} \mathrm{~m}^{3} \), and the pressure of the air in it is \( 8.5 \times 10^{6} \mathrm{~Pa} \). Assume that air is a diatomic ideal gas whose internal energy \( U \) is given by \( U=\frac{5}{2} n R T \). If one home uses \( 30.0 \mathrm{~kW} \) h of energy per day, how many homes could this internal energy serve for one day?