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A body cools down from 45°C to 40°C in 5 minutes and to 35°C in another 8 minutes. Find the temperature of the surrounding.

A body cools down from 45°C to 40°C in 5 minutes and to 35°C in another 8 minutes. Find the temperature of the surrounding.

Grade:12

1 Answers

Arun
25750 Points
5 years ago
50°C 45°C 35°C
Surrounding temperature is ‘T’°C Avg.
t = 50 + 45/2 = 47.5 Avg. temp.  
Variation from surrounding T = 47.5 – T  
Degree of drop in temp = 50 – 45/5 = 1 °C/mm  
By Network’s Law 1°C/mm = bA * t ⇒ bA = 1/t = 1/47.5 – T …(1)  
In second case,  
Avg, temp = 35 + 45/2 = 57.5 Avg. temp.  
Variation from surrounding t’ = 57.5 – t
 rate of fall of temp = 45 – 35/8 = 40.625 °C/mm  
By Network’s Law ⇒ 5/B = 1/(47.5 - T) * (57.5 - T)
 By Componendo & Dividendo method  
We get,  
T = 34.1°C
 
 

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