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QNEET-2016-Ph-1144: NEET 2016 Physics - Class 11 NEET-2016-Ph-1144 Solution: A body cools from a temperature 3T to 2T in 10 minutes. The…
A body cools from a temperature 3T to 2T in 10 minutes. The room temperature is T. Assume that Newton's law of cooling is applicable. The temperature of the body at the end of next 10 minutes will be T
Multiple Choice Options
- A 4 7 _ T
- B 2 3 _ T
- C 3 4 _ T
- D T
Step-by-Step Verified Solution
According to Newton�s law of cooling,
d T d t = K ( T _ T s )
For two cases,
d T 1 d t = K ( T 1 _ T s )
and d T 2 d t = K ( T 2 _ T s )
Here, T s = T , T 1 = 3 T + 2 T 2 = 2.5 T
and d T 1 d t = 3 T _ 2 T 10 = T 10
T 2 = 2 T + T _ 2 and d T 2 d t = 2 T _ T _ 10
So T 10 = K ( 2.5 T _ T ) ...(i)
2 T _ T _ 10 = K ( 2 T + T _ 2 _ T ) ...(ii)
Dividing eqn. (i) by eqn. (ii), we get
T 2 T _ T _ = ( 2.5 T _ T ) ( 2 T + T _ 2 _ T )
2 T + T _ 2 _ T = ( 2 T _ T _ ) _ 3 2
T _ = 3 ( 2 T _ T _ ) _ 4 T _ = 6 T
_ T _ = 3 2 T