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Water is boiled in a container having a bottom of surface area 25 cm2, thickness 0.1 mm and thermal conductivity 50 W/m-°C. 100 g of water is converted into steam per minute in the steady state after the boiling starts. Assuming that no heat is lost to the atmosphere, calculate the temperature of the lower surface of the bottom. Latent heat of vaporization of water = 2.26 × 106 J/kg.

Water is boiled in a container having a bottom of surface area 25 cm2, thickness 0.1 mm and thermal conductivity 50 W/m-°C. 100 g of water is converted into steam per minute in the steady state after the boiling starts. Assuming that no heat is lost to the atmosphere, calculate the temperature of the lower surface of the bottom. Latent heat of vaporization of water = 2.26 × 106 J/kg.

Grade:upto college level

1 Answers

Deepak Patra
askIITians Faculty 471 Points
8 years ago
Sol. A = 25 cm^2 = 25 × 10^–4 m^2 l = 1 mm = 10^–3 m K = 50 w/m-°C| Q/t = Rate of conversion of water into steam = 100 * 10^-3 * 2.26 * 10^6/1 min = 10^-1 * 2.26 * 10^6/60 = 0.376 = 10^4 Q/t = KA(θ base 1 – base 2)/l ⇒ 0.376 * 10^4 = 50 * 25 * 10^-4 * (θ - 100)/10^-3 ⇒ θ = 10^-3 * 0.376 * 10^4/50 * 25 * 10^-4 = 10^5 * 0.376/50 * 25 = 30.1 = 30

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