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A cup of hot coffee is initially at 70 ° C and is left in a room that has a temperature
20 ° C environment. Assume that from time t = 0 it cools at a rate of 10 °C per minute.

How long does it take for hot coffee to cool to a temperature of 25 ° C?

Using T(t) TA (TA To)e kt where TA initial temperature and T(t) is the temperature in the time t environment temperature, To

Respuesta :

Answer:

It will take 4 minutes and 30 seconds for hot coffee to cool to a temperature of 25 ° C

Step-by-step explanation:

This problem can be modeled by a first order equation

T(t) = TA + kt

In which TA is the temperature at instant zero and r is the rate of warming(g>0) or cooling(k<0). t is the time in minutes.

The initial temperature of the cup of coffee is 70ºC. So TA = 70. The temperature cools  at the rate of 10ºC per minute, so k = -10. So, the equation of the model is:

T(t) = 70 - 10t

We want to know the instant of time when T = 25, so:

25 = 70 - 10t

10t = 70 - 25

10t = 45

t = 4.5 minutes

It will take 4 minutes and 30 seconds for hot coffee to cool to a temperature of 25 ° C

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