A typical scuba tank has a volume V of 10 liters. When fully charged, it contains compressed air at a pressure of 200 bars, or 2.0 x 10^7 Pa.
a) What is the uncompressed volume of the air if the ambient pressure is 1000hPa and the temperature is 293K for both the compressed and uncompressed air?
b) How much mechanical work in joules is required to fill the tank, if the process is isothermal? Hint: Recall that the pressure p will be a function of V, and consider the starting and ending volumes as your limits of integration.
c) If the compressor is able to deliver 1000W of average power, how long does it take to fill the tank?