a) As a result of losing heat to the medium by conduction the temperature of the
ID: 2186812 • Letter: A
Question
a) As a result of losing heat to the medium by conduction the temperature of the body will change. Argue that dT/dt = - B(T-T1). This result is known as Newton's law of cooling. Explain why one might expect that
B~kl/C, where l is the linear extent of the object and C its heat capacity.
b) If the object has temperature T0 at t=0, show that T(t)=T1+(T0-T1)e^-Bt .
Explanation / Answer
a. This is what is observed in nature rate of heat transfer between two bodies is proportional to temp. diff. between these bodies i.e higher the diff. higher the rate of heat flow between atmosphere and body hence cooling. b. With dT/dt = -B(T-T1) => d(T-T1)/(T-T1) = -B dt Integrating both sides ln(T-T1) = -B t T(t) = T1 + e^-Bt with intial condition T(0) = T0 , T0 = T1 +1 hence the answer by writting 1 as T0-T1 infront of e^-Bt
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