A closed cubical box made of perfectly insulating material of thickness 8 cm and the only way for heat to enter or leave the box is through two solid, cylindrical, metallic plugs, each of cross-sectio

Question

A closed cubical box made of perfectly insulating material of thickness 8 cm and the only way for heat to enter or leave the box is through two solid, cylindrical, metallic plugs, each of cross-sectional area 12 cm² and length 8 cm in opposite walls of the box. The outer surface of one plug is kept at 100°C while the outer surface of the other plug is maintained at 4°C. The thermal conductivity of the plug is 50 cal s⁻¹ m⁻¹ K⁻¹. A source of energy generating 36 cal s⁻¹ is enclosed inside the box. Find the equilibrium temperature of the inner surface of the box, assuming that it is the same at all points on the inner surface.

Answer:

76

Solution:

$\frac{k A}{l} = \frac{50 \times 4.2 \times 12 \times 1 0 ^{- 4}}{0.08} = 3.15$ W/K per plug. Energy balance: $G (100 - T) + 36 \times 4.2 = G (T - 4)$ , so $T = \frac{100 + 4}{2} + \frac{151.2}{2 G} = 76.0^{\circ}$ C.

TestHub · Accepted Answer

l k A ​ = 0.08 50 × 4.2 × 12 × 1 0 − 4 ​ = 3.15 W/K per plug. Energy balance: G ( 100 − T ) + 36 × 4.2 = G ( T − 4 ) , so T = 2 100 + 4 ​ + 2 G 151.2 ​ = 76.0 ∘ C.

Physics - Heat & Thermo Question with Solution | TestHub

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