When steam at `100^@C` is passed into a metal cylinder, water at `100 ^@C` is collected at the rate of 200 g/min. If the area and thickness of cylinder are `300 cm^2` and 20 mm, respectively, determine the temperature of the outer surface. Take, thermal conductivity of metal `= 0.424 cal s^(-1)`cm. Latent heat of steam `= 540 cal g^(-1)`

Explanation

To solve the problem, we need to determine the temperature of the outer surface of a metal cylinder when steam at 100°C is passed through it, and water is collected at a rate of 200 g/min. We will use the given thermal conductivity of the metal and the latent heat of steam.

### Step-by-Step Solution:

1. **Calculate the Heat Released by the Steam:**
- The mass of steam collected per minute is 200 g.
- To convert this to grams per second, we divide by 60:
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