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Which expression gives the potential temperature?

  • A.T times the ratio of reference pressure to pressure raised to the power R over c sub p
  • B.T multiplied by the ratio of pressure to reference pressure raised to the power of the gas constant alone
  • C.T plus the lapse rate times height
  • D.T divided by the Exner function, which is defined as the pressure ratio raised to the power of gamma

Answer: A

Integrating the first law for an adiabatic process gives \( \theta = T (p_0/p)^{R/c_p} \), with the exponent equal to 0.286 for dry air. Equivalently temperature equals potential temperature times the Exner function. The exponent follows directly from the integration and is not an empirical constant, which is worth noticing because it makes the formula easy to reconstruct. A single measurement chosen to respond to the one asymmetry beats several that respond to shared behaviour.

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