A tall skyscraper has an official height of H 0 . Assume that this height was me

Question

A tall skyscraper has an official height of H0. Assume that this height was measured on a cool spring day when the temperature was T0. You could use the skyscraper as a sort of giant thermometer on a hot summer day by carefully measuring its height. Suppose you do this and discover that it is h taller than its official height, where h is much, much smaller than H0.

What is the expression for the temperature, T, assuming that the building is in thermal equilibrium with the air and that its entire frame is made of steel ( steel )? (your expression will contain  steel  - do not enter a numerical value)

I tried T= T(sub 0) + (h-H(sub 0))/(H(sub 0)(sub steel));

(h-H(sub 0))/(H(sub 0)(sub steel)) [Answer requires T(sub 0)];

and having just reread "h much much SMALLER than H(sub 0)"

T= T(sub 0) + (H(sub 0)-h)/(H(sub 0)(sub steel)).

Answer should be conceptual (the formula; no numbers). Only one more attempt allowed. Thanks

Explanation / Answer

h= H0*steel*(T-T0)

T= T0 + h/(H0*steel)

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