Hyperloop: Air compression

Classical Mechanics Level 3

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 intake rate of air is \(1.43~\mbox{kg/s}\). What is the rate of heat energy gain for the air during compression in Watts?

(The Hyperloop has a water cooling system to cool the air back down so that the air cushion system is not expelling incredibly hot air into the tunnel.)

Details and assumptions

  • Assume for this problem that the specific heat of air is \(1000~\mbox{J/kg K}\).

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