it takes 10 minutes to cool a liquid from 61 degree Celsius to 59 degree Celsius if room temperature is 30 degree Celsius and time taken in cooling from 51 degree Celsius to 49 degree Celsius
Answers
The time taken in cooling from 51 degree Celsius to 49 degree Celsius is 15 minutes.
Explanation:
According to Newton’s Law of Cooling, we have
dT/dt = k [T - To] ….. (i)
where
k = constant for the liquid
To = temperature of the surrounding i.e., the room temperature
T = temperature of the body
Based on the law in (i), we will solve both the cases by using the average method:
Case 1:
Temperature reduces from 61℃ to 59℃, so dT = 61 – 59 = 2℃
Time taken by the liquid to cool from 61℃ to 59℃, dt = 10 minutes
To = 30 ℃
Average temperature of the body, T = [61 + 59]/2 = 60℃
Therefore, substituting the values in (i), we get
2/10 = k [60 - 30]
⇒ k = 1/ [5*30] = 6.6 *10⁻³ ……. (ii)
Case 2:
Now, the temperature reduces from 51℃ to 49℃, so dT = 51 – 49 = 2℃
Average temperature of the body, T = [51 + 49]/2 = 50℃
Similarly, by using the eq.(i) and substituting the value of k from (ii) for case 2, we get
2/dt = 6.6*10⁻³ [50 - 30]
⇒ 2/dt = 6.6*10⁻³ * 20
⇒ dt = 2 / 0.133
⇒ dt = 15 minutes
Thus, the time taken in cooling from 51 ℃ to 49 ℃ is 15 minutes.
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