Steam at 100°C is passed into one end of a 10 mm thick and 200 \( \text{cm}^2 \) area copper cylinder. Water at 100°C is collected at the rate of 150 \( \text{g min}^{-1} \) at the other end of the cylinder. Find the temperature of the outer surface if the conductivity of copper is 0.8 \( \text{cal s}^{-1} \text{cm}^{-1}\text{°C} \) and the latent heat of steam is 540 \( \text{cal g}^{-1} \) .

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