A body cools in a surrounding of constant temperature 30^∘ C. It's heat capacity is 2 J / C. In

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A body cools in a surrounding of constant temperature 30^∘...

A body cools in a surrounding of constant temperature $30^{\circ} \mathrm{C}$. It's heat capacity is $2 \mathrm{~J} / \mathrm{C}$. Initial temperature of the body is $40^{\circ} \mathrm{C}$. Assume Newton's law of cooling is valid. The body cools to $36^{\circ} \mathrm{C}$ in 10 minutes. In further 10 minutes it will cool from $36 \mathrm{C}$ to (a) $34.8 \mathrm{C}$ (b) $32.1 \%$ (c) $32.8^{\circ} \mathrm{C}$ (d) $33.6^{\circ} \mathrm{C}$

A body cools in a surrounding of constant temperature $30^{\circ} \mathrm{C}$. It's heat capacity is $2 \mathrm{~J} / \mathrm{C}$. Initial temperature of the body is $40^{\circ} \mathrm{C}$. Assume Newton's law of cooling is valid. The body cools to $36^{\circ} \mathrm{C}$ in 10 minutes.
In further 10 minutes it will cool from $36 \mathrm{C}$ to
(a) $34.8 \mathrm{C}$
(b) $32.1 \%$
(c) $32.8^{\circ} \mathrm{C}$
(d) $33.6^{\circ} \mathrm{C}$

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Key Concepts

Differential Equations in Thermal Dynamics

Thermal processes like cooling are modeled using first-order differential equations that relate the rate of temperature change to the temperature difference with the environment. Solving these equations yields an exponential function that predicts temperature evolution over time.

Time Constant

The time constant is a parameter that represents the time it takes for the system to change significantly, such as reaching about 63% of the way from its initial temperature toward the ambient temperature. It determines the rate at which exponential decay occurs in a cooling process.

Newton's Law of Cooling

Newton's law of cooling states that the rate at which an object changes its temperature is proportional to the difference between its current temperature and the ambient temperature. This principle forms the basis for modeling thermal exchange processes and results in an exponential approach to equilibrium.

Exponential Decay

Exponential decay describes processes in which a quantity decreases at a rate proportional to its current value. When applied to cooling, it means that the temperature difference between an object and its surroundings decreases exponentially over time.

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