A body initially at 60^∘ C cools to 50^∘ C in 10 minutes. What will be its temperature at the en

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A body initially at 60^∘ C cools to 50^∘ C in 10 minutes....

A body initially at $60^{\circ} \mathrm{C}$ cools to $50^{\circ} \mathrm{C}$ in 10 minutes. What will be its temperature at the end of next 10 minutes, if the room temperature is $25^{\circ} \mathrm{C}$. Assume Newton's law of cooling : (a) $42.85^{\circ} \mathrm{C}$ (b) $45^{\circ} \mathrm{C}$ (c) $40.46^{\circ} \mathrm{C}$ (d) $44.23^{\circ} \mathrm{C}$

A body initially at $60^{\circ} \mathrm{C}$ cools to $50^{\circ} \mathrm{C}$ in 10 minutes. What will be its temperature at the end of next 10 minutes, if the room temperature is $25^{\circ} \mathrm{C}$. Assume Newton's law of cooling :
(a) $42.85^{\circ} \mathrm{C}$
(b) $45^{\circ} \mathrm{C}$
(c) $40.46^{\circ} \mathrm{C}$
(d) $44.23^{\circ} \mathrm{C}$

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Key Concepts

Newton's Law of Cooling

Newton's law of cooling states that the rate of change of temperature of an object is proportional to the difference between its own temperature and that of the surrounding environment. This principle explains the cooling (or heating) process as an exponential decay or growth toward the ambient temperature.

Exponential Decay in Temperature

In the context of Newton's law, the temperature of an object changes following an exponential decay model. This means that the temperature approaches the ambient temperature asymptotically, with the rate of cooling slowing down as the temperature difference decreases.

Cooling Constant

The cooling constant is a proportionality factor in the differential equation describing Newton's law of cooling. It determines how quickly the temperature difference between the object and its surroundings decreases over time and is typically derived from experimental data or given conditions.

Ambient Temperature

Ambient temperature refers to the constant temperature of the surrounding environment in which the object is placed. It is the baseline temperature that the object is approaching as it cools or heats, driving the evolution of the object's temperature according to Newton's law of cooling.

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