Question

Figure shows a rod of variable cross-section area. Two ends of rod is maintained at different temperature. Let radius of cross-section, where temperature is arithmetic mean of temperature at two ends be r. Then 'r' –

• A. Is equal to arithmetic mean of a and b
• B. Is equal to geometric mean of a and b
• C. Is equal to harmonic mean of a and b
• D. Depends upon length of rod, a and b

Answer 1

Answer: (C)

Is equal to harmonic mean of a and b

Answer 2

Let the cross-section be AA¢

\ R₁ = R₂

[R₁ = Thermal resistance of rod left of cross-section AA¢]

̃ $\frac{1}{a} - \frac{1}{r}$= $\frac{1}{r} - \frac{1}{b}$

̃ r = $\frac{2ab}{a + b}$