five hundred kcal of heat is added to 2-kg of water at 80⁰C. how much steam is produced?

To determine the amount of steam produced when 500 kcal of heat is added to 2 kg of water at 80°C, we need to understand the concept of specific heat capacity and latent heat of vaporization.

First, let's calculate the heat energy required to raise the temperature of the water from 80°C to its boiling point.

The specific heat capacity of water is approximately 1 calorie/gram. To convert kcal to calories, we multiply by 1000:
500 kcal = 500,000 calories.

Since we have 2 kg of water, which is equivalent to 2000 grams, and the change in temperature is 100°C (water's boiling point is 100°C), we can calculate the heat energy required to raise the temperature using the specific heat capacity formula:

Heat Energy = mass × specific heat capacity × change in temperature.

Heat Energy = 2000 g × 1 cal/g °C × 100°C = 200,000 calories or 200,000 kcal.

This means that 200,000 kcal of heat energy is needed to raise the temperature of the water from 80°C to its boiling point.

Now, let's calculate the heat energy required to vaporize the water.

The latent heat of vaporization for water is 540 kcal/kg.

To find the heat energy required to vaporize the water, we multiply the mass of water by the latent heat of vaporization:

Heat Energy = mass × latent heat of vaporization.

Heat Energy = 2 kg × 540 kcal/kg = 1,080 kcal.

Therefore, the total heat energy required to heat the water from 80°C to its boiling point and vaporize it is 200,000 kcal + 1,080 kcal = 201,080 kcal.

Finally, we can convert the total heat energy to the amount of steam produced.

The heat energy required to convert one kilogram of water to steam is 540 kcal. Therefore, we can divide the total heat energy by the latent heat of vaporization to find the amount of steam produced:

Amount of steam = total heat energy / latent heat of vaporization.

Amount of steam = 201,080 kcal / 540 kcal/kg = 372.52 kg of steam.

Hence, when 500 kcal of heat is added to 2 kg of water at 80°C, approximately 372.52 kg of steam is produced.

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