# On a typical summer evening the temperature was 90°F at 7:00 PM. At 8:00 A.M. the next morning the temperature was 70.5 F. What is the average rate of change in temperature?

May 16, 2017

1.5 (""^oF)/(hr)

#### Explanation:

I wouldn't necessarily call this a chemistry-related question, but it doesn't matter, I'll help.

The average rate of change of temperature with respect to time in this case can be represented by the equation

${\left(\Delta {T}^{o}\right)}_{a v} = \frac{\Delta {T}^{o}}{\Delta t}$

where

${\left(\Delta {T}^{o}\right)}_{a v}$ is the average rate of change of temperature with time,

$\Delta {T}^{o}$ is the total change in temperature over the time period

and $\Delta t$ is the total change in time

The total change in temperature over the time period is

${90}^{o} F - {70.5}^{o} F = \ast {19.5}^{o} F \ast$

and the total time change is

$20 : 00$ (for convenience) $- 7 : 00 = \ast 13 h r \ast$

Plugging values into the equation, we have

(DeltaT^o)_(av) = (DeltaT^o)/(Deltat) = (19.5 ^oF)/(13hr) = 1.5 (""^oF)/(hr)