Below θ0 is the temperature of the enclosure.
By Newton's law of cooling, during the cooling from 80 to 70°C, where θ1=80°C,θ2=70°C,dt=5 min:
dtdθ=C(θ−θ0), dtθ1−θ2=C(2θ1+θ2−θ0), 2=C(75−θ0).
Cooling from 70 to 62°, where θ1=70°C,θ2=62°C,dt=5 min:
dtdθ=C(θ−θ0), dtθ1−θ2=C(2θ1+θ2−θ0), 1.6=C(66−θ0). Divide one equation by another:
1.62=C(66−θ0)C(75−θ0), θ0=30°C. In this problem, we put
θ=2θ1+θ2 because we need to use the average temperature of the system during the given interval.
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