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Which exponent appears in the definition of potential temperature?

  • A.The gas constant divided by the specific heat at constant pressure, about 0.286
  • B.The ratio of the specific heats at constant pressure and constant volume, which is about 1.4 for dry air
  • C.The reciprocal of the scale height
  • D.The ratio of the latent heat of vaporisation to the product of the gas constant and the temperature involved

Answer: A

The exponent \( R/c_p \) equals 287 divided by 1005, or about 0.286, and it follows directly from integrating the first law for an adiabatic process. It is sometimes written as kappa. The ratio of specific heats gamma equals 1.4 and is related but distinct, since \( R/c_p = (\gamma-1)/\gamma \). Confusing the two is a frequent source of error.

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