# 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.
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