How much heat (in kJ) will it take to bring 56 kg of ice at -8°C to dry steam? Answer to 3 significant figures
do this in phases
a. heating ice to 0C (mcdeltaT)
b. meltting ice m*Hf
c. heating water: mc deltaTemp
d. making steam: m*Hv
add the heats.
To find the amount of heat required to bring ice at -8°C to dry steam, we need to go through several steps.
Step 1: Calculate the heat required to raise the temperature of ice from -8°C to 0°C.
The heat required to raise the temperature of a substance can be calculated using the formula:
Q = m * c * ΔT
Where:
Q = heat energy (in Joules)
m = mass of the substance (in kilograms)
c = specific heat capacity of the substance (in J/kg°C)
ΔT = change in temperature (in °C)
For ice, the specific heat capacity is approximately 2.09 J/g°C, which is equivalent to 2090 J/kg°C.
Converting the mass of ice from 56 kg to grams:
56 kg * 1000 g/kg = 56000 g
Calculating the heat required to raise the temperature of ice from -8°C to 0°C:
Q1 = 56000 g * 2090 J/kg°C * (0°C - (-8°C))
Step 2: Calculate the heat required to melt ice at 0°C.
The heat required to melt a substance can be calculated using the formula:
Q = m * Hf
Where:
Q = heat energy (in Joules)
m = mass of the substance (in kilograms)
Hf = heat of fusion of the substance (in J/kg)
For ice, the heat of fusion is approximately 334,000 J/kg.
Calculating the heat required to melt ice:
Q2 = 56000 g * 334000 J/kg
Step 3: Calculate the heat required to raise the temperature of water from 0°C to 100°C.
Using the same formula as in Step 1, but with the specific heat capacity of water (c = 4.18 J/g°C or 4180 J/kg°C), we can calculate the heat required to raise the temperature of water:
Q3 = 56000 g * 4180 J/kg°C * (100°C - 0°C)
Step 4: Calculate the heat required to boil water and convert it to steam at 100°C.
The heat required to boil a substance is calculated using the formula:
Q = m * Hv
Where:
Q = heat energy (in Joules)
m = mass of the substance (in kilograms)
Hv = heat of vaporization of the substance (in J/kg)
For water, the heat of vaporization is approximately 2,260,000 J/kg.
Calculating the heat required to boil water:
Q4 = 56000 g * 2260000 J/kg
Step 5: Calculate the total heat required.
The total heat required is the sum of all the individual heats calculated in the previous steps:
Total Q = Q1 + Q2 + Q3 + Q4
Converting the total heat from Joules to kilojoules, we divide by 1000:
Total Q (in kJ) = (Q1 + Q2 + Q3 + Q4) / 1000
Performing the calculations, we get:
Q1 = 56000 g * 2090 J/kg°C * 8°C = 930,560,000 J
Q2 = 56000 g * 334000 J/kg = 18,704,000,000 J
Q3 = 56000 g * 4180 J/kg°C * 100°C = 234,320,000 J
Q4 = 56000 g * 2260000 J/kg = 126,560,000,000 J
Total Q = 930,560,000 J + 18,704,000,000 J + 234,320,000 J + 126,560,000,000 J
Total Q = 145,428,880,000 J
Total Q (in kJ) = 145,428,880,000 J / 1000 = 145,428,880 kJ
Rounding to 3 significant figures, the amount of heat required to bring 56 kg of ice at -8°C to dry steam is approximately 145,000,000 kJ.