A cup of coffee at temperature cools in a room whose constant temperature is
PHYSICS · Single correct · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter
Problem
A cup of coffee at temperature T(t) cools in a room whose constant temperature is Ta. The rate of change of the coffee’s temperature is proportional to T(t)−Ta. Which statement about the constant of proportionality k is most consistent with the coffee cooling toward room temperature?
(a) k>0 since the proportionality constant is typically taken positive in Newton’s law of cooling.
(b) ∣k∣<1 so the exponential decay of temperature occurs slowly rather than instantaneously.
(c) k<0 because dtdT must be negative when T(t)>Ta.
(d) k=0 because the coffee eventually reaches thermal equilibrium.