Question

You are asked to design a cylindrical steel rod 50.0 cm long, with a circular cross section, that will conduct 170.0 J/s from a furnace at 350.0 ∘C to a container of boiling water under 1 atmosphere.

Answer 1

Answer:

You are asked to design a cylindrical steel rod 50.0 cm long, with a circular cross section, that will conduct 170.0 J/s from a furnace at 350.0 ∘C to a container of boiling water under 1 atmosphere.

Explanation:

Given Values:

L = 50 cm = 0.5 m

H = 170 j/s

To find the diameter of the rod, we have to find the area of the rod using the following formula.

Here Tc = 100.0° C

        k  = 50.2

       H = k × A × $\frac{[T_{H -}T_{C} ] }{L}$

Solving for A

       A  =  $\frac{H * L }{k * [ T_{H}- T_{C} ] }$

       A  = $\frac{170 * 0.5}{50.2 * [ 350 - 100 ]}$

       A  = $\frac{85}{12550}$ = 6.77 ×$10^{-3}$ m²

Now Area of cylinder is :

     A =  $\frac{\pi }{4}$ d²

solving for d:

    d =  $\sqrt{\frac{4 * 0.00677 }{\pi } }$

    d  = 9.28 cm