The expression of the Newton's law of cooling is given by, −
dT
dt
=k′(T−T0) Integrate the equation on both sides. ∫
dT
T−T0
=k′∫dt loge(T−T0)=−k′t ln(T−T0)=−k′t So,T=e−k′t+T0 for t→∞ And, T=T0 for T→∞ Hence, the temperature of the body varies exponentially with the time from T to T0 Thus the graph of T verses t is shown below.