Q.Why does a metal bar appear hotter than a wooden bar at the same temperature? Equivalently it also appears cooler than wooden bar if they are both colder than room temperature.

Key Idea: Thermal Conductivity and Rate of Heat Transfer.

Reasoning:

1. Metals possess significantly higher thermal conductivity compared to wood, which is a poor conductor of heat.
2. When a metal bar is hotter than your hand, its high thermal conductivity enables it to transfer heat to your hand at a much faster rate than a wooden bar at the same temperature. This rapid heat influx causes a more intense sensation of heat.
3. Conversely, when a metal bar is colder than your hand, its high thermal conductivity allows it to draw heat away from your hand at a much faster rate than a wooden bar. This rapid heat loss from your hand creates a more intense sensation of cold. …

Our perception of how "hot" or "cold" an object feels is not solely determined by its absolute temperature. Instead, it is primarily governed by the rate at which heat energy is transferred between the object and our skin. Our skin's temperature receptors are highly sensitive to this rate of heat flow. A rapid influx of heat into our skin registers as "very hot," while a rapid outflow of heat from our skin registers as "very cold."

The key property that dictates this rate of heat transfer through a material is its thermal conductivity.

1. Understanding Thermal Conductivity:

   Thermal conductivity is a measure of a material's ability to conduct heat. Materials with high thermal conductivity allow heat to flow through them quickly and efficiently. Materials with low thermal conductivity, often called thermal insulators, resist the flow of heat, meaning heat moves through them slowly.

2. Comparing Metal and Wood:

   Metals are excellent thermal conductors. Their atomic structure, particularly the presence of free electrons, allows for very efficient transfer of thermal energy. Wood, on the other hand, is a poor thermal conductor (a good insulator). Its cellular structure traps air, which is itself a poor conductor, significantly reducing its overall thermal conductivity.

3. Case 1: Objects Hotter Than Skin Temperature:

   Imagine both a metal bar and a wooden bar are at the same temperature, say $50^\circ\text{C}$, which is hotter than your skin temperature (approximately $37^\circ\text{C}$).

   • When you touch the metal bar, heat rapidly flows from the hotter metal to your cooler skin due to metal's high thermal conductivity. This quick and substantial transfer of heat into your skin triggers a strong "hot" sensation, making the metal feel very hot.
   • When you touch the wooden bar, heat also flows from the wood to your skin. However, because wood has low thermal conductivity, this heat transfer occurs much more slowly. Your skin receives heat at a lower rate, resulting in a less intense "hot" sensation, making the wood feel less hot, or even just warm, by comparison.

4. Case 2: Objects Colder Than Skin Temperature:

   Now, consider both bars at the same temperature, say $10^\circ\text{C}$, which is colder than your skin temperature. This scenario also applies if they are "colder than room temperature," assuming room temperature is below skin temperature. …

The precise physical quantity here is thermal effusivity, $e=\sqrt{k\rho c}$, which sets how fast a surface's temperature responds when touched — conductivity alone is only part of the story. When your hand (at roughly $34°C$) contacts an object, the interface briefly settles at a temperature governed by the relative effusivities of skin and object; a high-effusivity material (metal) pulls that interface strongly toward its own bulk temperature, so touching hot metal feels closer to its true, higher temperature and touching cold metal feels closer to its true, lower temperature. Wood's low effusivity means the interface stays closer to your skin's own temperature reg …