Hyperloop: Compressor work

The Hyperloop is a hypothetical new fast transport system between cities, which works by launching pods that carry people through a very low air pressure tunnel. The Hyperloop reduces friction between the pods and the tunnel by supporting the pod on a cushion of air. This air is gathered through the front of the pod and compressed from the initial ambient pressure and temperature of $99~\mbox{Pa}$ and $293~\mbox{K}$ to $2.1~\mbox{kPa}$ and $857~\mbox{K}$ . The rate of air compressed in this way is $0.49~\mbox{kg/s}$ and the total compressor input power is $276~\mbox{kW}$ . We define the efficiency $\eta$ of the compressor as the (work done on the gas)/(input work to the compressor). If the pressure as a function of volume during the compression is $P= AV^{-\alpha}$ , where $A$ and $\alpha$ are constants, what is the efficiency of the compressor?

• The molar mass of air is $29~\mbox{g/mol}$ .
• Ignore any change in the bulk kinetic energy of the air.