Water with a mass of 1000kg leaves a hose at 20oC and is converted by the heat from the fire into steam at 300oC. List the steps needed in order to determine the amount of heat that is added to the water. For each step show the formula that must be used and replace the variables with the appropriate numbers. Also, state whether the heat for each step will be positive or negative. You do not need to complete the calculations. Specific heat of water = 4.2 kJ/kgoC, Latent heat of vaporization of water = 2260 kJ/kg, Specific heat of steam = 2.0 kJ/kgoC

Question

Water with a mass of 1000kg leaves a hose at 20oC and is converted by the heat from the fire into steam at 300oC. List the steps needed in order to determine the amount of heat that is added to the water. For each step show the formula that must be used and replace the variables with the appropriate numbers. Also, state whether the heat for each step will be positive or negative. You do not need to complete the calculations. Specific heat of water = 4.2 kJ/kgoC, Latent heat of vaporization of water = 2260 kJ/kg, Specific heat of steam = 2.0 kJ/kgoC

Answer 1

To determine the amount of heat that is added to the water and converted into steam, we need to consider the following steps:

Step 1: Calculate the heat required to increase the temperature of the water from 20°C to its boiling point.

Formula: Q1 = m * c * ΔT

For this step, we need to use the specific heat capacity of water (c) and the temperature change (ΔT).
c = 4.2 kJ/kg°C (specific heat of water)
m = 1000 kg (mass of water)
ΔT = boiling point - initial temperature = 100°C - 20°C = 80°C

Since we are increasing the temperature, the heat (Q1) will be positive.

Step 2: Calculate the heat required for the phase change from liquid water to steam.

Formula: Q2 = m * L

For this step, we need to use the latent heat of vaporization of water (L).
L = 2260 kJ/kg (latent heat of vaporization of water)
m = 1000 kg (mass of water)

During a phase change, the heat (Q2) is absorbed without changing the temperature, so it will be positive.

Step 3: Calculate the heat required to increase the temperature of the steam from its boiling point to the final temperature of 300°C.

Formula: Q3 = m * c * ΔT

For this step, we'll use the specific heat capacity of steam (c) and the temperature change (ΔT).
c = 2.0 kJ/kg°C (specific heat of steam)
m = 1000 kg (mass of steam)
ΔT = final temperature - boiling point = 300°C - 100°C = 200°C

Since we are increasing the temperature, the heat (Q3) will be positive.

Step 4: Add up the heat from all three steps to get the total amount of heat added to the water:

Total heat added = Q1 + Q2 + Q3

Remember to account for the signs of each heat value when summing them up.

By following these steps and plugging in the given values, you can determine the amount of heat that is added to the water without actually completing the calculations.