contestada

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?

Respuesta :

Answer:

Part a)

[tex]T = 13.8 degree C[/tex]

Part b)

[tex]t = 68.54 min[/tex]

Explanation:

As per Newton's law of cooling we know that

[tex]\frac{dT}{dt} = k(T - T_s)[/tex]

now we will have

[tex]\int \frac{dT}{T - T_s} = K\int dt[/tex]

now we will have

[tex]ln(\frac{T - T_s}{T_1 - T_s}) = kt[/tex]

now we will have

[tex]T = T_s + (T_1 - T_s)e^{kt}[/tex]

so we will have

[tex]T_1 = 5 degree[/tex]

now we will have

[tex]10 = 20 + (5 - 20)e^{k(25)}[/tex]

[tex]e^{25k} = 0.67[/tex]

Now we have

k = -0.016

now after 55 min

[tex]T = 20 + (5 - 20)e^{55 k}[/tex]

[tex]T = 13.8 degree C[/tex]

Part b)

now when temperature is 15 degree C

then we will have

[tex]15 = 20 + (5 - 20)e^{kt}[/tex]

[tex]5 = 15 e^{kt}[/tex]

[tex]kt = -1.098[/tex]

[tex]t = 68.54 min[/tex]

Otras preguntas