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Which one of the following statements is FALSE?

  • A.For an ideal gas, the enthalpy is independent of pressure.
  • B.For a real gas going through an adiabatic reversible process, the process equation is given by \(PV^{\gamma}\) = constant, where \(P\) is the pressure, \(V\) is the volume and \(\gamma\) is the ratio of the specific heats of the gas at constant pressure and constant volume.
  • C.For an ideal gas undergoing a reversible polytropic process \(PV^{1.5}\) = constant, the equation connecting the pressure, volume and temperature of the gas at any point along the process is \(\dfrac{P}{R} = \dfrac{mT}{V}\), where \(R\) is the gas constant and \(m\) is the mass of the gas.
  • D.Any real gas behaves as an ideal gas at sufficiently low pressure or sufficiently high temperature.

Answer: B

The FALSE statement is the one claiming that a real gas in an adiabatic reversible process follows \(PV^{\gamma}\) = constant.

The relation \(PV^{\gamma}\) = constant is derived from the first law using \(PV = mRT\) and constant specific heats, so it holds for an ideal (perfect) gas only. A real gas, whose equation of state and specific heats differ from the ideal ones, does not follow it in general.

The other statements are true. An ideal gas's enthalpy depends on temperature alone, so it is independent of pressure. The equation \(P/R = mT/V\) is just \(PV = mRT\) rearranged; the ideal gas equation holds at every state, whatever polytropic process (here \(PV^{1.5}\) = constant) connects them. And any real gas approaches ideal behaviour at low pressure or high temperature, where molecular volume and attraction become negligible.

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