Question

The ratio of thermal conductivity of two rods of different materials is 5:4. The two rods of the same area of cross-section and the same thermal resistance will have the lengths in the ratio:

A) 4:5
B) 9:1
C) 1:9
D) 5:4

Answer 1

The lengths of two rods with the same thermal resistance but different thermal conductivities in the ratio of 5:4 will have their lengths in the inverse ratio, which is 4:5.

Step-by-step explanation:

The student provided a ratio of thermal conductivity for two rods made of different materials as 5:4. To find the lengths' ratio for the same thermal resistance, we can use the formula for thermal resistance, which is R = ℓ/kA, where ℓ is the length of the rod, k is the thermal conductivity, and A is the cross-sectional area. Since the cross-sectional areas are the same and the rods have the same thermal resistance, we can say that the product of thermal conductivity (k) and length (ℓ) for both rods must be equal. Therefore, if the ratio of thermal conductivity (k) is 5:4, the ratio of lengths (ℓ) must be the inverse which is 4:5.