The ratio of thermal conductivity of two rods of different material is 5 : 4. The two rods of same area of cross-section and same thermal resistance will have the lengths in the ratio
Thermal conductivity is a property of a material that measures its ability to conduct heat. It quantifies the rate at which heat flows through a material due to a temperature gradient. Materials with high thermal conductivity transfer heat quickly while those with low thermal conductivity act as insulators and reduce heat transfer.
Class 11 Physics Chapter 10 Thermal Properties of Matter explains heat transfer specific heat capacity thermal expansion and calorimetry. It covers conduction convection and radiation along with thermal equilibrium and laws of heat transfer. This chapter is essential for understanding thermodynamics and its practical applications in the CBSE Exam 2024-25.
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The thermal resistance (R) of a rod is given as:
R = L / (kA)
where:
L is the length of the rod,
k is the thermal conductivity,
A is the cross-sectional area.
Given two rods made of different materials, having equal thermal resistance: R₁ = R₂, and the area of cross-section: A₁ = A₂, we obtain:
L₁ / (k₁A) = L₂ / (k₂A)
Area of cross-section cancels out:
L₁ / k₁ = L₂ / k₂
Rearranging to get the ratio of lengths:
L₁ / L₂ = k₁ / k₂
k₁ : k₂ = 5 : 4
L₁ : L₂ = 4 : 5
Answer: 4 : 5
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