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

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To determine how much steam is produced when 500 kcal of heat is added to 2 kg of water at 80°C, we need to follow a few steps:

1. Calculate the heat energy required to raise the temperature of the water from 80°C to its boiling point.
2. Calculate the heat energy required to convert the water at its boiling point to steam.
3. Convert the total heat energy into the corresponding amount of steam produced.

Step 1: Calculate the heat energy to raise the temperature:
The specific heat capacity of water is approximately 4.186 J/(g·°C).
Using the equation Q = mcΔT, where Q is the heat energy, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature, we can calculate the heat energy required to raise the temperature of the water:
Q1 = m1cΔT1

m1 = 2 kg (mass of water)
c = 4.186 J/(g·°C) = 4186 J/(kg·°C) (specific heat capacity of water)
ΔT1 = boiling point of water - initial temperature = 100°C - 80°C = 20°C

Substituting these values:
Q1 = 2 kg × 4186 J/(kg·°C) × 20°C = 167,440 J

Step 2: Calculate the heat energy to convert water to steam:
The heat of vaporization of water is approximately 2260 kJ/kg.
Using the equation Q = mL, where Q is the heat energy, m is the mass, and L is the latent heat of vaporization, we can calculate the heat energy required to convert the water to steam:
Q2 = m2L

m2 = 2 kg (mass of water)
L = 2260 kJ/kg = 2260 x 10^3 J/kg (latent heat of vaporization of water)

Substituting these values:
Q2 = 2 kg × 2260 x 10^3 J/kg = 4,520,000 J

Step 3: Convert the total heat energy into steam produced:
To find the amount of steam produced, we need to convert the total heat energy (Q1 + Q2) into calories and then divide by the latent heat of vaporization of steam.

To convert Joules into kcal:
1 kcal = 4184 J
Total heat energy in kcal = (Q1 + Q2) / 4184

Total heat energy in kcal = (167,440 J + 4,520,000 J) / 4184 = 1071.77 kcal

The latent heat of vaporization of steam is approximately 540 kcal/kg.
To calculate the mass of steam produced, we divide the total heat energy by the latent heat of vaporization of steam:
Mass of steam = Total heat energy / Latent heat of vaporization of steam

Mass of steam = 1071.77 kcal / 540 kcal/kg = 1.988 kg

Therefore, approximately 1.988 kg of steam is produced when 500 kcal of heat is added to 2 kg of water at 80°C.