COMEDK2025PhysicsThermal Properties of MatterActual
The rate of heat conduction in the given two metal rods having the same length is found to be the same when the temperature difference between the ends is kept 30^ C If the area of cross section of the first rod is 8 10⁻² ~m ^2 then what will be area of cross section of the second rod? [ Given that the ratio of the thermal conductivity of the first rod to that of the second rod is 1: 4 ]
Options
- A4 10⁻² ~m ^2
- B2 10⁻² ~m ^2
- C4 10⁻⁴ ~m ^2
- D2 10⁻⁴ ~m ^2
Correct answer
B. 2 10⁻² ~m ^2
Step-by-step solution
The rate of heat conduction H through a rod is given by the formula H = KA T L , where K is the thermal conductivity, A is the area of cross-section, T is the temperature difference, and L is the length of the rod. Given that the rate of heat conduction is the same for both rods, we have H₁ = H₂ . Substituting the formula for both rods: K₁ A₁ T₁ L₁ = K₂ A₂ T₂ L₂ Since the lengths L₁ = L₂ and the temperature differences T₁ = T₂ = 30^ C are the same, the equation simplifies to: K₁ A₁ = K₂ A₂ Rearranging to solve for