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Which form does the barometric formula take for a constant lapse rate?

  • A.A logarithmic decrease in which the pressure falls by equal amounts for each doubling of the height reached
  • B.A power law in temperature
  • C.An exponential in height, which is the form appropriate to an atmosphere of uniform temperature throughout
  • D.A linear decrease

Answer: B

With temperature falling linearly with height, integration gives pressure proportional to the temperature raised to the power \( g/(R\Gamma) \), where \( \Gamma \) is the lapse rate. For the standard value of 6.5 kelvin per kilometre that exponent is about 5.26. The exponential form applies only to the isothermal case, which is a good approximation in the lower stratosphere. A limit that survives making every external component ideal is an intrinsic one, and worth knowing for that reason.

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