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

Answer:

Part a)

$T = 13.8 degree C$

Part b)

$t = 68.54 min$

Explanation:

As per Newton's law of cooling we know that

$\frac{dT}{dt} = k(T - T_s)$

now we will have

$\int \frac{dT}{T - T_s} = K\int dt$

now we will have

$ln(\frac{T - T_s}{T_1 - T_s}) = kt$

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

$15 = 20 + (5 - 20)e^{kt}$

$5 = 15 e^{kt}$

$kt = -1.098$

$t = 68.54 min$