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The temperature of a body falls from 50oC to 40oC in 10 minutes. If the temperature of the surroundings is 20oC Then temperature of the body after another 10 minutes will be
- a)36.6oC
- b)33.3oC
- c)35oC
- d)30oC
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The temperature of a body falls from 50oC to 40oC in 10 minutes. If th...
Given data:
Initial temperature of the body (T1) = 50oC
Final temperature of the body (T2) = 40oC
Temperature of surroundings (To) = 20oC
Time interval = 10 minutes
Formula used:
Newton's Law of Cooling states that the rate of change of temperature of an object is directly proportional to the difference between its temperature and the temperature of its surroundings.
Calculation:
1. Calculate the rate of change of temperature (k):
T1 - To = (T2 - To)e^(-kt)
50 - 20 = (40 - 20)e^(-10k)
30 = 20e^(-10k)
1.5 = e^(-10k)
-ln(1.5) = -10k
k ≈ 0.0513
2. Calculate the temperature after another 10 minutes:
T = To + (T1 - To)e^(-kt)
T = 20 + (50 - 20)e^(-0.0513*10)
T ≈ 33.3oC
Therefore, the temperature of the body after another 10 minutes will be 33.3oC, which is option 'B'.
Initial temperature of the body (T1) = 50oC
Final temperature of the body (T2) = 40oC
Temperature of surroundings (To) = 20oC
Time interval = 10 minutes
Formula used:
Newton's Law of Cooling states that the rate of change of temperature of an object is directly proportional to the difference between its temperature and the temperature of its surroundings.
Calculation:
1. Calculate the rate of change of temperature (k):
T1 - To = (T2 - To)e^(-kt)
50 - 20 = (40 - 20)e^(-10k)
30 = 20e^(-10k)
1.5 = e^(-10k)
-ln(1.5) = -10k
k ≈ 0.0513
2. Calculate the temperature after another 10 minutes:
T = To + (T1 - To)e^(-kt)
T = 20 + (50 - 20)e^(-0.0513*10)
T ≈ 33.3oC
Therefore, the temperature of the body after another 10 minutes will be 33.3oC, which is option 'B'.
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The temperature of a body falls from 50oC to 40oC in 10 minutes. If the temperature of the surroundings is 20oC Then temperature of the body after another 10 minutes will bea)36.6oCb)33.3oCc)35oCd)30oCCorrect answer is option 'B'. Can you explain this answer?
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