AIIMS 2007 Physics Thermal Conductivity Assertion Reason Question

To understand the given question, we need to analyze both the assertion and the reason in the context of thermal conductivity and heat transfer.

Assertion

The assertion states: "A brass tumbler feels much colder than a wooden tray on a chilly day." This is accurate because metals like brass have high thermal conductivity, meaning they can transfer heat rapidly. When you touch a brass tumbler, it quickly draws heat away from your skin, making it feel colder compared to a wooden tray, which is a poor conductor of heat.

Reason

The reason given is: "The thermal conductivity of brass is more than the thermal conductivity of wood." This statement is indeed true. The thermal conductivity ($k$) of materials quantifies their ability to conduct heat. For brass, $k$ is typically around $120 \, \text{W/m·K}$, whereas for wood, $k$ can vary but is generally around $0.1 \, \text{W/m·K}$. This significant difference in thermal conductivities explains why brass feels colder.

Correct Answer Explanation

The correct answer is A) Both Assertion and Reason are true and Reason is the correct explanation of Assertion. The reason accurately explains the assertion: the high thermal conductivity of brass leads to a rapid heat transfer from your hand to the brass tumbler, making it feel colder.

Why Other Options Are Incorrect

• B) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion. This option is incorrect because the reason directly supports the assertion. The high thermal conductivity of brass does explain why it feels colder.

• C) Assertion is true but Reason is false. This option is incorrect because both the assertion and reason are true. The thermal conductivity of brass is indeed greater than that of wood.

• D) Both Assertion and Reason are false. This option is incorrect as both statements are true.

Relevant Concepts

Thermal conductivity is defined by the equation:

$$Q = k \cdot A \cdot \frac{\Delta T}{d}$$

where:

• $Q$ is the rate of heat transfer (in watts),
• $k$ is the thermal conductivity of the material,
• $A$ is the cross-sectional area through which heat is being transferred,
• $\Delta T$ is the temperature difference between the two surfaces,
• $d$ is the thickness of the material.

In the context of our discussion, the high value of $k$ for brass means that even a small temperature difference ($\Delta T$) will result in a significant rate of heat transfer compared to wood.

Conclusion

In summary, both the assertion and reason in the question are true, and the reason clearly explains the assertion. Thus, the correct answer is option A. Understanding thermal conductivity helps clarify why different materials feel differently at the same temperature, particularly in terms of heat transfer and sensation.