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A hot baked potato is taken out of a hot oven at $T=T_1(C).$ Room temperature is given as $T_a.$ Assume that potato is spherical in shape with physical properties $,c_p.$ Surface coefficient of heat transfer by convection is $h(\frac{W}{m^{20}}C).$ Calculate the temperature of potato as a function of time.

$-$Newton's law of cooling $($the rate of heat loss from the surface of the potato is proportional to the temperature difference between the potato and the surrounding environment$)$

Energy balance $($The energy lost by the potato$)$

Obtain the ODE

State the initial condition: $T(0)=?$

Solve the ODE