Question

The temperature of liquid in an experiment starts at 0*C. The experiment calls for the temperature of the liquid to change at a rate of -0.60*C per minute. How long will it take for the liquid to reach -10.5*C

Answer 1

The liquid will take 17.5 minutes to reach -10.5 ºC.

Explanation:

From this statement we understand that the temperature of liquid is increased at constant rate in time, whose model is described by:

`T (t) = \dot r \cdot t + T_(o)` (Eq. 1)

Where:

`T` - Temperature of the liquid, measured in degrees Celsius.

`\dot r` - Heating rate, measured in degrees Celsius per minute.

`t` - Time, measured in minutes.

`T_(o)` - Initial temperature, measured in degrees Celsius.

If we know that
`\dot r = -0.60\,(^(\circ)C)/(min)` and
`T_(o) = 0\,^(\circ)C`, the temperature model for the liquid is:

`T(t) = -0.60\cdot t` (Eq. 2)

In addition, if
`T(t) = -10.5\,^(\circ)C`, then time taken for the liquid to reach that temperature is:

`t = (-10.5)/(-0.60)`

`t = 17.5\,min`

The liquid will take 17.5 minutes to reach -10.5 ºC.