Kelvi

Certain quantity of water cools from $70^{\circ}C$ to $60^{\circ}C$ in the first $5$ min and to $54^{\circ}C$ in the next $5$ min. The temperature of the surroundings is

hard

Thermal Properties of Matter

2014

physics

$45^{\circ}C$

$20^{\circ}C$

$42^{\circ}C$

Explanation

To solve this problem, we will use Newton's Law of Cooling, which states that the rate of change of temperature of an object is proportional to the difference between its temperature and the ambient temperature (surroundings). $\\$ The formula for Newton's Law of Cooling is: $\\ \frac{dT}{dt} = -k(T - T_s) \\$

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Certain quantity of water cools from 70∘C 70^{\circ}C 70∘C to 60∘C 60^{\circ}C 60∘C in the first 5 5 5 min and to 54∘C 54^{\circ}C 54∘C in the next 5 5 5 min. The temperature of the surroundings is

Explanation

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Certain quantity of water cools from $70^{\circ}C$ to $60^{\circ}C$ in the first $5$ min and to $54^{\circ}C$ in the next $5$ min. The temperature of the surroundings is