Question

solve the differential equations by laplace theorem

A sphere of 3cm in diameter will be cooled by a chain of
air at a temperature of 100 ° C (T∞). The EDO that represents this heat transfer is:

mCp dT/dt= α(T-T∞)As=32

being α = 1000W /m^2Kthe air convection coefficient. Also being the initial temperature
equal to 298K and the properties of the sphere are(m=0,045kg;cp=1600;As=0,11m^2)
(Find the algebraic expression that
represents Temperature as a function of time. Trace T x t

answer:T(t) = 298 e^ 0,0153x – (-343,40 + 343,40e^ 0,0153x)

Answer 1