Question

When a cold drink is taken from a refrigerator, its temperature is 5°C. After 25 minutes in a 20°C room its temperature has increased to 10°C. (Round your answers to two decimal places.) (a) What is the temperature of the drink after 55 minutes? 13.853 Correct: Your answer is correct. °C (b) When will its temperature be 15°C?

Answer 1

Part a)

`T = 13.8 degree C`

Part b)

`t = 68.54 min`

Step-by-step explanation:

As per Newton's law of cooling we know that

`(dT)/(dt) = k(T - T_s)`

now we will have

`\int (dT)/(T - T_s) = K\int dt`

now we will have

`ln((T - T_s)/(T_1 - T_s)) = kt`

now we will have

`T = T_s + (T_1 - T_s)e^(kt)`

so we will have

`T_1 = 5 degree`

now we will have

`10 = 20 + (5 - 20)e^(k(25))`

`e^(25k) = 0.67`

Now we have

k = -0.016

now after 55 min

`T = 20 + (5 - 20)e^(55 k)`

`T = 13.8 degree C`

Part b)

now when temperature is 15 degree C

then we will have

`15 = 20 + (5 - 20)e^(kt)`

`5 = 15 e^(kt)`

`kt = -1.098`

`t = 68.54 min`