Isometric view of a solid copper object is shown below. If a constant heat source of \(100^\circ\)C is applied at the point \(P\) continuously, which point on the solid will reach the temperature of the heat source the earliest? Neglect heat losses and assume point \(P\) lies on an equilateral triangle.
Show Hint
For heat-conduction problems in solids:
\begin{itemize}
\item Heat reaches points with minimum thermal resistance first,
\item Shorter distance and larger cross-section speed up conduction,
\item Material uniformity simplifies comparison to geometry alone.
\end{itemize}
Step 1: Heat conduction in a homogeneous solid (copper) depends primarily on:
\begin{itemize}
\item Shortest conduction path,
\item Cross-sectional area available for heat flow,
\item Absence of bottlenecks or constrictions.
\end{itemize}
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Step 2: Since heat losses are neglected, the point that will reach the source temperature earliest is the one with the least thermal resistance between it and point \(P\).
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Step 3: Examine the geometry:
\begin{itemize}
\item Points A and B lie across a narrower section with reduced cross-sectional area, slowing heat flow.
\item Point D is farther from \(P\) along a longer and thicker path.
\item Point C lies closest to \(P\) through the most direct path with comparatively larger conducting area.
\end{itemize}
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Step 4: Hence, heat reaches point C earlier than the other points.
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Final Answer:
\[
\boxed{C}
\]
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