The temperature T of a body cooling in an environment, whose unknown ambient temperature is , is

The temperature T of a body cooling in an environment, whose unknown ambient temperature is α, is given by

where T₀ is the initial temperature of the body and k is a physical constant. To determine the value of α, the temperature of the body is recorded at two times, t₁ and t₂, where t₂ = 2t₁ and T(t₁) = T₁, T(t₂) = T₂. Show that

Transcribed Image Text:

T(t) = a + (Toa)e-kt