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A body cools from 50•C to 48•Celsius in 5sec.how long will it take to cool from 40•C to 39•C? Assume the temp. Of surrounding to be 30.0•c and Newton's law of cooling to be valid.?
a)2.5s
b)10s
c)20s
d)5s?
a)2.5s
b)10s
c)20s
d)5s?
Most Upvoted Answer
A body cools from 50•C to 48•Celsius in 5sec.how long will it take to ...
Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Using this law, we can solve the problem using the following steps:
Step 1: Calculate the cooling constant
We first need to calculate the cooling constant, which is given by the formula k = (1/t)*ln[(T1-Ts)/(T0-Ts)], where k is the cooling constant, t is the time taken for the temperature to decrease by (T1-T0), T1 is the initial temperature, T0 is the final temperature, and Ts is the temperature of the surroundings.
Using the given values, we get k = (1/5)*ln[(50-30)/(48-30)] = 0.198 s^-1
Step 2: Calculate the time taken to cool from 40•C to 39•C
We can use the formula T(t) = Ts + (T0 - Ts)*e^(-kt), where T(t) is the temperature at time t.
We need to find the time taken for the temperature to decrease from 40•C to 39•C. Substituting the values, we get:
39 = 30 + (40-30)*e^(-0.198t)
9 = 10*e^(-0.198t)
ln(0.9) = -0.198t
t = ln(0.9)/(-0.198) = 10.05 s
Therefore, the time taken to cool from 40•C to 39•C is 10.05 s.
Answer: b) 10s
Step 1: Calculate the cooling constant
We first need to calculate the cooling constant, which is given by the formula k = (1/t)*ln[(T1-Ts)/(T0-Ts)], where k is the cooling constant, t is the time taken for the temperature to decrease by (T1-T0), T1 is the initial temperature, T0 is the final temperature, and Ts is the temperature of the surroundings.
Using the given values, we get k = (1/5)*ln[(50-30)/(48-30)] = 0.198 s^-1
Step 2: Calculate the time taken to cool from 40•C to 39•C
We can use the formula T(t) = Ts + (T0 - Ts)*e^(-kt), where T(t) is the temperature at time t.
We need to find the time taken for the temperature to decrease from 40•C to 39•C. Substituting the values, we get:
39 = 30 + (40-30)*e^(-0.198t)
9 = 10*e^(-0.198t)
ln(0.9) = -0.198t
t = ln(0.9)/(-0.198) = 10.05 s
Therefore, the time taken to cool from 40•C to 39•C is 10.05 s.
Answer: b) 10s
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A body cools from 50•C to 48•Celsius in 5sec.how long will it take to ...
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A body cools from 50•C to 48•Celsius in 5sec.how long will it take to cool from 40•C to 39•C? Assume the temp. Of surrounding to be 30.0•c and Newton's law of cooling to be valid.?a)2.5sb)10sc)20sd)5s?
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A body cools from 50•C to 48•Celsius in 5sec.how long will it take to cool from 40•C to 39•C? Assume the temp. Of surrounding to be 30.0•c and Newton's law of cooling to be valid.?a)2.5sb)10sc)20sd)5s? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A body cools from 50•C to 48•Celsius in 5sec.how long will it take to cool from 40•C to 39•C? Assume the temp. Of surrounding to be 30.0•c and Newton's law of cooling to be valid.?a)2.5sb)10sc)20sd)5s? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body cools from 50•C to 48•Celsius in 5sec.how long will it take to cool from 40•C to 39•C? Assume the temp. Of surrounding to be 30.0•c and Newton's law of cooling to be valid.?a)2.5sb)10sc)20sd)5s?.
A body cools from 50•C to 48•Celsius in 5sec.how long will it take to cool from 40•C to 39•C? Assume the temp. Of surrounding to be 30.0•c and Newton's law of cooling to be valid.?a)2.5sb)10sc)20sd)5s? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A body cools from 50•C to 48•Celsius in 5sec.how long will it take to cool from 40•C to 39•C? Assume the temp. Of surrounding to be 30.0•c and Newton's law of cooling to be valid.?a)2.5sb)10sc)20sd)5s? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body cools from 50•C to 48•Celsius in 5sec.how long will it take to cool from 40•C to 39•C? Assume the temp. Of surrounding to be 30.0•c and Newton's law of cooling to be valid.?a)2.5sb)10sc)20sd)5s?.
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