In a cylindrical metallic vessel some water is taken and is put on a burner. The bottom surface area of the vessel is 2.5 × 1 0 − 3 m² and thickness 1 0 − 3 m. The thermal conductivity of the metal of

Question

In a cylindrical metallic vessel some water is taken and is put on a burner. The bottom surface area of the vessel is $2.5 \times 1 0^{- 3}$ m² and thickness $1 0^{- 3}$ m. The thermal conductivity of the metal of vessel is 50 W/m°C. When water boils, it is observed that 100 gm water is vaporized per minute. Calculate the temperature of the bottom surface of the vessel. Given that the latent heat of vaporization of water is $2.26 \times 1 0^{6}$ J/kg.

Answer:

130.10

Solution:

$P = \frac{0.1 \times 2.26 \times 1 0 ^{6}}{60} = 3767$ W. $Δ T = \frac{P d}{k A} = \frac{3767 \times 1 0 ^{- 3}}{50 \times 2.5 \times 1 0 ^{- 3}} = 30.1$ , so the bottom is at $130.1^{\circ}$ C.

TestHub · Accepted Answer

P = 60 0.1 × 2.26 × 1 0 6 ​ = 3767 W. Δ T = k A P d ​ = 50 × 2.5 × 1 0 − 3 3767 × 1 0 − 3 ​ = 30.1 , so the bottom is at 130.1 ∘ C.

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