The left end of a copper rod (length = 20 cm area of cross-section = 0.20cm2) is maintained at 20°C and the right end is maintained at 80°C. Neglecting any loss of heat through radiation find (a) the temperature at a point 11 cm from the left end and (b) the heat current through the rod. Thermal conductivity of copper = 385 W m−1°C−1.

Engineering

Physics

SI Units

Conduction of Heat

Thermal Expansion

Question

The left end of a copper rod (length = 20 cm area of cross-section = 0.20cm²) is maintained at 20°C and the right end is maintained at 80°C. Neglecting any loss of heat through radiation find (a) the temperature at a point 11 cm from the left end and (b) the heat current through the rod. Thermal conductivity of copper = 385 W m^−1°C⁻¹.

LiveFree JEE Main Previous Year Online Papers Live Free JEE Advance Previous Year Online Papers

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

t = 20cm = 20 × 10⁻²m

A = 0.2m²= 0.2 × 10⁻⁴m²

θ₁= 80°C

θ₂= 20°C K = 385

(a) Constant heat current follow through the wire, temperature gradient

$C = \frac{dt}{L} = \frac{80 - 20}{20} = 3^{\circ} C / cm$

For 11 cm fro left end,

T = 20 + C × 11

T = 20 + 3 × 11 = 53°C

(b) $\frac{Q}{t} = \frac{KA (θ_{1} - θ_{2})}{ℓ} = \frac{385 \times 0.2 \times 10^{- 4} (80 - 20)}{20 \times 10^{- 2}} = 2.31$