A frozen chicken at $0 ^ { \circ } \mathrm { C }$ is taken out of the freezer and placed on a table at $20 ^ { \circ } \mathrm { C }$ . One hour later the temperature of the chicken is $18 ^ { \circ } \mathrm { C }$ . The mathematical model for the temperature $T ( t )$ as a function of time $t$ is (assuming Newton's law of warming)
A) $\frac { d T } { d t } = k T , T ( 0 ) = 0 , T ( 1 ) = 18$
B) $\frac { d T } { d t } = k ( T - 20 ) , T ( 0 ) = 0 , T ( 1 ) = 18$
C) $\frac { d T } { d t } = ( T - 20 ) , T ( 0 ) = 0 , T ( 1 ) = 18$
D) $\frac { d T } { d t } = T , T ( 0 ) = 0 , T ( 1 ) = 18$
E) $\frac { d T } { d t } = k ( T - 18 ) , T ( 0 ) = 0 , T ( 1 ) = 18$

Question

Quizplus · Accepted Answer

Newton's law of cooling (or warming) states that the rate of temperature change of an object is proportional to the difference between its own temperature and the ambient temperature. Here, the ambient temperature is $20^\circ C$, and the initial condition is $T(0) = 0^\circ C$ (the temperature of the chicken when taken out of the freezer). After one hour ($t = 1$), the temperature of the chicken is $18^\circ C$, so $T(1) = 18$. Thus, the correct model is $\frac{dT}{dt} = k(T - 20), T(0) = 0, T(1) = 18$, which matches choice B.

A Frozen Chicken At 0∘C0 ^ { \circ } \mathrm { C }0∘C

A Frozen Chicken At $0 ^ { \circ } \mathrm { C }$