Question

In an experiment to verify Newton's law of cooling, the temperature of hot water in a calorimeter
T/oC
is plotted against time t/min. Which of the following is true about the graph?
the graph is linear and parallel to the T-axis
the slope of the graph is positive
the slope of the graph is negative
the graph is hyperbola

Answer 1

Answer on Question #57999, Physics / Molecular Physics | Thermodynamics

In an experiment to verify Newton's law of cooling, the temperature of hot water in a calorimeter $T / ^0 C$ is plotted against time t/min. Which of the following is true about the graph?

the graph is linear and parallel to the T-axis

the slope of the graph is positive

the slope of the graph is negative

the graph is hyperbola

Solution:

Newton's Law of Cooling states that the rate at which convection cools a hot object is proportional to the temperature difference between the hot object and the ambient (room) temperature.

This is stated mathematically as

$$\frac {d T}{d t} = - k (T - T _ {a m b i e n t})$$

Since this cooling rate depends on the instantaneous temperature (and is therefore not a constant value), this relationship is an example of a 1st order differential equation. The constant $k$ in this equation is called the cooling constant. The solution to this differential equation is

$$T (t) = T _ {f i n a l} + \left(T _ {o} - T _ {f}\right) e ^ {- k t}$$

Temperature vs Time

Answer: the slope of the graph is negative

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