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Which form does the first law take for an atmospheric parcel?

  • A.Heat added equals the work done
  • B.Heat added equals the change in the potential energy of the parcel as it is lifted through the atmosphere
  • C.Heat added equals the specific heat at constant pressure times temperature change minus alpha times pressure change
  • D.Heat added equals the specific heat at constant volume multiplied by the change in the temperature alone

Answer: C

Writing the law in terms of enthalpy gives \( dq = c_p dT - \alpha dp \), where alpha is the specific volume, and this is the form used throughout meteorology. It is convenient because atmospheric parcels change pressure as they move vertically. Setting the heat term to zero and substituting hydrostatic balance immediately gives the dry adiabatic lapse rate. A limit that survives making every external component ideal is an intrinsic one, and worth knowing for that reason.

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