Read before you solve · 3 min

Read Variable Conductivity: Integrate the Temperature Equation

This short read prepares one exact NSEP pattern: steady conduction with k proportional to 1/t. Identify the physical condition before calculating.

NSEP · Thermal Physics · 1 linked question · 100% coverage

Know this first

Steady Conduction with k Proportional to 1/T is the central idea in this question pattern. Identify the condition in the stem before applying the method below.

Study deeper: NCERT Physics · Thermal Physics

Start with the physical model

Read the configuration once, state the conserved quantity or governing law, and mark any changing geometry, sign convention or limiting condition.

Build the relation

Here K = \alpha /T

In steady state, heat flux J is constant and

J = -K dT/dx = -(\alpha /T)dT/dx

Thus dT/ T = -(J/α)dx, so lnT varies linearly with x

Using the temperature values as specified in the problem, T(x)=Tcold(Thot/Tcold)x/L.

At 0.50 m from the cold end:

T = 10×91/4=17.32°C (A)

At 0.50 m from the hot end:

T = 10\times 93/4=51.96°C (B). |J|=(\alpha /L)\ln (90/10)=(\alpha /2)ln9≈1.10\alpha (C)

Since |dT/dx|=|J|T/α, the gradient magnitude is larger near the hotter end (D). All are correct.

Check before selecting

Check units, sign and one limiting case. A valid result must still fit the original geometry and stated constraint.

OlympIQ exam lens

✓Name the governing law before using a formula.
✓Keep the stated geometry and direction information explicit.
✓Use one unit or limiting-case check.

OlympIQ trap

A linear temperature profile applies only when thermal conductivity is constant.

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