Calculating the Final Temperature of Mixed Water and Steam

When dealing with the mixing of superheated steam and water, the process involves several steps, including temperature adjustments, condensation, and heat transfer. This article explores these steps in detail and provides the necessary calculations to determine the final temperature of the mixture.

Understanding the Components and Initial Conditions

Consider a scenario where 10 kg of water is at 120 degrees Celsius (superheated steam) is mixed with 20 kg of water at 40 degrees Celsius. The initial conditions are as follows:

Step 1: Cooling the Superheated Steam

The first step involves cooling the superheated steam from 120°C to 100°C. The specific heat of steam is approximately 0.48 kcal/kg·°C. The heat required to cool 10 kg of steam from 120°C to 100°C can be calculated as:

Heat lost by steam mass × specific heat × change in temperature

Heat lost by steam 10 kg × 0.48 kcal/kg·°C × 20°C 96 kcal

Step 2: Condensing the Steam

Next, we need to condense 10 kg of steam at 100°C to water at 100°C. The latent heat of condensation for water is approximately 540 kcal/kg. The heat released during condensation is:

Heat released by condensation mass × latent heat of condensation

Heat released by condensation 10 kg × 540 kcal/kg 5400 kcal

The total heat that can be released by condensing the steam is 96 kcal (from cooling) 5400 kcal (from condensation) 5496 kcal.

Step 3: Heating the Water

The next step is to determine whether the 20 kg of water at 40°C can absorb all the heat released during the condensation process. The specific heat of water is 1 kcal/kg·°C. The maximum heat that can be absorbed by heating 20 kg of water to 100°C is:

Heat required to heat water mass × specific heat × change in temperature

Heat required to heat water 20 kg × 1 kcal/kg·°C × 60°C 1200 kcal

Since the total heat available (5496 kcal) is much greater than the heat required to raise the temperature of the 20 kg of water to 100°C (1200 kcal), only a portion of the steam will condense. Consequently, the final temperature of the mixture will remain at 100°C.

Conclusion

In summary, when 10 kg of superheated steam at 120°C is mixed with 20 kg of water at 40°C, the final temperature of the mixture will be 100°C. This is because the heat released during the condensation of the steam is sufficient to heat a portion of the water to 100°C, but not all of it, leaving the temperature of the system at 100°C.