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Which approximation gives virtual temperature from mixing ratio \( w \)?

  • A.T times one plus 0.61 w
  • B.T divided by one plus 0.61 w, since the moist air is less dense than the corresponding sample of dry air
  • C.T times 0.61 w
  • D.T plus 0.61 w expressed in kelvin, with the mixing ratio taken in grams per kilogram of the dry air present

Answer: A

Expanding the exact expression for small mixing ratio gives \( T_v \approx T(1+0.61w) \), where \( w \) is in kilograms per kilogram. The coefficient 0.61 is \( (1-\epsilon)/\epsilon \). With \( w \) of 20 grams per kilogram and \( T \) of 300 kelvin the correction is about 3.7 kelvin, which is a substantial buoyancy effect and explains why virtual temperature matters for convection. Most errors here come from carrying a result across from a neighbouring case where it does not hold.

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