Question

Which of the following statement is wrong?

• A. The heat transfer in liquid and gases takes place according to convection
• B. The amount of heat flow through a body is dependent upon the material of the body
• C. The thermal conductivity of solid metals increases with rise in temperature
• D. Logarithmic mean temperature difference is not equal to the arithmetic mean temperature difference.

Hint:

For most pure metals, both electrical conductivity and thermal conductivity decrease as temperature rises because of increased electron-phonon scattering.
Always read "Which statement is wrong?" questions carefully to avoid picking a correct statement by mistake.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks to identify the incorrect (wrong) statement among the four options regarding heat transfer mechanisms and thermal properties.

Step 2: Detailed Explanation:

• Statement A: Heat transfer in fluids (liquids and gases) primarily occurs via convection, where bulk fluid motion transports heat. This is a correct statement.

• Statement B: Fourier's Law of Heat Conduction states that heat flow rate ($Q = -k A \frac{dT}{dx}$) depends on the thermal conductivity ($k$), which is a characteristic property of the material of the body. This is a correct statement.

• Statement C: In solid metals, thermal energy is conducted primarily by free electrons and lattice vibrations (phonons).
As temperature increases, the thermal scattering of free electrons by the vibrating lattice ions increases significantly.
This increased scattering decreases the mean free path of the electrons, which generally causes the thermal conductivity ($k$) of most pure metals (like copper, aluminum) to decrease with a rise in temperature. Thus, Statement C is incorrect, making it the correct option for this "find the wrong statement" question.

• Statement D: The Logarithmic Mean Temperature Difference (LMTD) and Arithmetic Mean Temperature Difference (AMTD) are mathematically distinct: \[ \text{LMTD} = \frac{\Delta T_1 - \Delta T_2}{\ln(\Delta T_1 / \Delta T_2)} \neq \frac{\Delta T_1 + \Delta T_2}{2} \] LMTD is always less than AMTD. This is a correct statement.

Step 3: Final Answer:
The incorrect statement is (C) "The thermal conductivity of solid metals increases with rise in temperature".