Question

# In a surrounding medium of temperature of 1$$0^{\circ}C$$, a body takes $$7$$ min for a fall of temperature from $$60^{\circ}C$$ to $$40^{\circ}C$$. In what time the temperature of the body will fall from $$40^{\circ}C$$ to $$28^{\circ}C$$?

A
7 min
B
11 min
C
14 min
D
21 min

Solution

## The correct option is B 7 minNewton’s Law of Cooling states that the rate fall of temperature of the body is proportional to the difference between the temperature of the body and that of the surrounding medium.Thus $$\dfrac{\theta_2-\theta_1}{t}=K(\dfrac{\theta_1+\theta_2}{2}-\theta_0)$$$$\implies \dfrac{60-40}{7}=K(\dfrac{60+40}{2}-10)$$and $$\dfrac{40-28}{t}=K(\dfrac{40+28}{2}-10)$$Solving the two equations gives $$t=7min$$Physics

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