Two bodies each having a heat capacity of C=500 J / K are joined together by a rod of length L=

step 1 Dear students, in problem 11 of chapter 11 we have asked that two bodies each having heat capaci

Two bodies each having a heat capacity of C=500 J / K are...

Two bodies each having a heat capacity of $C=500 \mathrm{~J} / \mathrm{K}$ are joined together by a rod of length $L=40.0 \mathrm{~cm}$, thermal conductivity $20 \mathrm{~W} / \mathrm{mK}$, and cross-sectional area of $S=3.00 \mathrm{~cm}^{2}$. The bodies are joined with the help of a thermally insulated rod. The time after which temperature difference diminishes $\eta=2$ times is (Disregard the heat capacity of the rod.) (A) $193 \mathrm{~min}$ (B) $240 \mathrm{~min}$ (C) $77 \mathrm{~min}$ (D) $144 \mathrm{~min}$

Two bodies each having a heat capacity of $C=500 \mathrm{~J} / \mathrm{K}$ are joined together by a rod of length $L=40.0 \mathrm{~cm}$, thermal conductivity $20 \mathrm{~W} / \mathrm{mK}$, and cross-sectional area of $S=3.00 \mathrm{~cm}^{2}$. The bodies are joined with the help of a thermally insulated rod. The time after which temperature difference diminishes $\eta=2$ times is (Disregard the heat capacity of the rod.)
(A) $193 \mathrm{~min}$
(B) $240 \mathrm{~min}$
(C) $77 \mathrm{~min}$
(D) $144 \mathrm{~min}$

Key Concepts

Exponential Decay of Temperature Difference

When two bodies are coupled thermally, the difference in their temperatures often decays exponentially over time. This concept incorporates the system’s time constant, which is derived from the combined effect of the bodies’ heat capacities and the thermal conductance of the connector, allowing prediction of the rate at which temperature differences diminish.

Thermal Resistance

Thermal resistance is analogous to electrical resistance and represents the opposition to heat flow in a material. It depends on the material’s length, conductivity, and cross-sectional area, and helps in evaluating the time constant in heat transfer problems.

Thermal Conductivity

Thermal conductivity is a material property that measures its ability to conduct heat. A higher thermal conductivity means that the material can transfer heat more efficiently, which is crucial for determining the speed of heat transfer in the given setup.

Fourier's Law of Heat Conduction

This law states that the rate of heat transfer through a material is proportional to the temperature gradient and the properties of the material, such as thermal conductivity and cross-sectional area. It forms the basis for calculating how quickly heat flows through a conductor like a rod between two bodies.

Heat Capacity

Heat capacity quantifies the amount of heat required to change a body's temperature by a given amount. In thermal systems involving energy exchange between bodies, it determines how the stored thermal energy affects the rate of temperature change.

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