 Solution

The actual Earth response to doubling carbon dioxide is expected to be much smaller than this roughly $60\mathrm{K}$ all-grey-absorbers estimate. Carbon dioxide absorbs in selected spectral bands rather than doubling opacity across the entire thermal spectrum, and doubling it does not double the other infrared absorbers. Saturated band centres and overlap with water absorption further distinguish it from uniform opacity multiplication. Changes in water vapour, clouds and the lapse rate introduce important climate feedbacks, but do not justify treating the real atmosphere as the stipulated dry, wavelength-independent absorber. The idealized number is therefore not an estimate of real-world equilibrium climate sensitivity.