Question

The rate of flow of heat (Q), through a conductor, depends on the coefficient of thermal conductivity (σ), area of cross section (A), temperature difference across the two ends of the rod (Δθ), and the length (Δl) of the conductor. The relevant formula

\(Q=σA\frac{Δ\theta}{Δl}\)

is used to determine σ experimentally. The relative percentage errors, in the measurement of different quantities, are as follow: 

Flowing heat energy = 2% 

Time for which heat flows = 0.2% 

Temperature difference = 2% 

Length of the rod = 0.5% 

Area of cross section of the rod = 0.5%

The relative percentage error, in the determination of σ , would be

(1) 0.2%

(2) 5.2%

(3) 0.4%

(4) 2.6%

Answer 1

(2) 5.2%

The relation

\(Q=σA\frac{Δ\theta}{Δl}\)

can be rewritten as

\(σ=(\frac{ΔH}{Δl}).\frac{Δl}{Δ\theta}\)  \((∵Q=\frac{ΔH}{Δt})\)

∴ \(\frac{Δσ}{σ}=\frac{ΔH}{H}+\frac{Δt}{t}+\frac{Δ(Δ\theta)}{Δ\theta}+\frac{ΔA}{A}\)

= 2% + 0.2% + 0.5% + 2% + 0.5% 

= 5.2%