= Solution
{c}
The <dew-point depression> is $6\,\mathrm K$, so
$$
\boxed{z_{\rm LCL}\simeq125\times6\,\mathrm m=750\,\mathrm m.}
$$
Keeping $T_{D,s}=276.15\,\mathrm K$, $H\simeq158.5\,\mathrm{km}$ and $c_p=1004\,\mathrm{J\,kg^{-1}\,K^{-1}}$ gives approximately $747\,\mathrm m$, consistent with the rounded estimate.
The real <cloud> base can differ because <entrainment> changes the parcel's <atmospheric mixing ratio> and <temperature>, surface <humidity> varies, and the environmental <pressure> profile need not match the assumed parcel profile. Finite <cloud-droplet activation> requires some <atmospheric supersaturation>, so the first visible <cloud droplets> need not occur exactly at the thermodynamic <lifting condensation level>. A parcel must also actually be lifted that far; environmental <static stability> can prevent this. The constant-<latent heat> and first-order <Taylor expansion> approximations produce smaller numerical differences.
Back to article page
