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Year 4 of the physics course of the University of Oxford

Physics of atmospheres and oceans course of the University of Oxford

Past exam of the physics of atmospheres and oceans course of the University of Oxford

2022

{c}

At the <Köhler activation radius>, the two coefficients satisfy
$$
S_c-1=\frac{2A}{3r_c},\qquad
A=\frac32r_c(S_c-1).
$$
Converting the <atmospheric supersaturation> to a fraction gives $S_c-1=0.004$, not $0.4$. Hence
$$
A=\frac32(2.0\times10^{-7}\,\mathrm m)(0.004)
=1.2\times10^{-9}\,\mathrm m,
$$
and the supplied curvature coefficient gives the <temperature>
$$
\boxed{T=\frac{3.3\times10^{-7}\,\mathrm{K\,m}}{1.2\times10^{-9}\,\mathrm m}
=275\,\mathrm K\simeq1.9\,{}^\circ\mathrm C.}
$$
The coefficient and the stated radius consistently use a radius convention; replacing radius by diameter without changing the coefficient would introduce a factor-of-two error.

Solution

Past exam of the physics of atmospheres and oceans course of the University of Oxford / 2022 / 3 / d / Solution

Past exam of the physics of atmospheres and oceans course of the University of Oxford / 2022 / 3 / d / Solution

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Past exam of the physics of atmospheres and oceans course of the University of Oxford / 2022 / 3 / d / Solution

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