Compressed air can be pumped underground into huge caverns as a form of energy storage. The volume of a cavern is 5.60 105 m3, and the pressure of the air in it is 8.40 106 Pa. Assume that air is a diatomic ideal gas whose internal energy U is given by U = 5/2 nRT. If one home uses 14.0 kWh of energy per day, how many homes could this internal energy serve for one day?

Question

Compressed air can be pumped underground into huge caverns as a form of energy storage. The volume of a cavern is 5.60  105 m3, and the pressure of the air in it is 8.40  106 Pa. Assume that air is a diatomic ideal gas whose internal energy U is given by U = 5/2 nRT. If one home uses 14.0 kWh of energy per day, how many homes could this internal energy serve for one day?

bobpursley · Answer

Well, PV=nRT, so U= 5/2PV. That will be in Joules. To convert to kWh (kJ3600sec), divide by 1000, then divide by 3600. That will be the energy in kWh of stored energy.