Question

In the steady state of temperature, the flow of heat across the body depends upon its:
A. thermal capacity
B. thermal conductivity
C. temperature difference across its opposite faces
D. thermal resistivity
Choose the CORRECT answer from the options given below:

• A. A,B and D only
• B. A,B and C only
• C. A, B, C and D
• D. B, C and D only

Hint:

Think of the analogy with electrical circuits (Ohm's Law, \(I = V/R\)): - Heat Flow \(H \leftrightarrow\) Current \(I\) - Temperature Difference \(\Delta T \leftrightarrow\) Voltage \(V\) - Thermal Resistance \(R_T = L/(kA) \leftrightarrow\) Electrical Resistance \(R\) Thermal capacity is analogous to electrical capacitance, which is irrelevant for steady DC current.

Answer 1

The Correct Option is D

Step 1: State Fourier's Law of Heat Conduction. For steady-state heat flow (\(H\) or \(\frac{dQ}{dt}\)), the formula is: \[ H = -kA \frac{dT}{dx} \] For a slab of thickness L, cross-sectional area A, and temperature difference \(\Delta T\), this simplifies to: \[ H = \frac{kA\Delta T}{L} \] where \(k\) represents thermal conductivity.
Step 2: Examine equation components. Heat flow \(H\) is influenced by:- k (thermal conductivity): This corresponds to statement B.- \(\Delta T\) (temperature difference): This corresponds to statement C.- Geometric factors (A and L).Thermal resistivity (\(\rho_T\)) is the inverse of thermal conductivity (\(\rho_T = 1/k\)). Since \(H\) depends on \(k\), it also depends on \(\rho_T\), validating statement D.Thermal capacity (\(C = mc\), with c as specific heat) governs heat storage for temperature changes. It does not affect the steady-state rate of heat flow, as temperatures are constant. Therefore, statement A is incorrect.
Step 3: Identify contributing factors. Steady-state heat flow is determined by thermal conductivity (B), temperature difference (C), and thermal resistivity (D).