 Solution

ID: past-exam-of-the-physics-of-atmospheres-and-oceans-course-of-the-university-of-oxford/2022/3/d/solution

S_{c} - 1 = \frac{2 A}{3 r _{c}}, A = \frac{3}{2} r_{c} (S_{c} - 1) .

S_{c} - 1 = 0.004

, not

0.4

. Hence

A = \frac{3}{2} (2.0 \times 1 0^{- 7} m) (0.004) = 1.2 \times 1 0^{- 9} m,

T = \frac{3.3 \times 1 0 ^{- 7} K m}{1.2 \times 1 0 ^{- 9} m} = 275 K ≃ 1.9^{\circ} 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.

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