1. The problem statement, all variables and given/known data A small adiabatic air compressor is used to pump air into a 20-m3 insulated tank. The tank initially contains air at 25°C and 101.33 kPa, exactly the conditions at which air enters the compressor. The pumping process continues until the pressure in the tank reaches 1,000 kPa. If the process is adiabatic and if compression is isentropic, what is the shaft work of the compressor? Assume air to be an ideal gas for which CP = (7/2)R and CV = (5/2)R. 2. Relevant equations 3. The attempt at a solution I derived the relationship for the enthalpy of an adiabatic as dH = V dp However, I also know ΔH = CpΔT When I calculate the two enthalpies, I get different answers for the change in enthalpy, which I know should be equal to the isentropic work. First off, how do I know my equation is only for an adiabatic and isentropic process, and would not work for something that is anisentropic and adiabatic? I realize the change in enthalpy is the change in molar enthalpy times the number of moles, but the number of moles is changing throughout the process until it reaches 1000 kPa. The other expression seems to bypass worrying about that. I am wondering which one, if either, is correct and why? In other words, how do I calculate ''isentropic enthalpy change'' vs. enthalpy change that is not isentropic?