calculate the total amount of heat needed to change 500g of ice at -10*C into 500g of steam at 120*C. do this by calculating the ehat required for each of the following steps and adding to get the total:
step 1. ice (-10C)-> ice (0C)
step 2. ice (0C) -> water (0C)
step 3. water (0C) -> water (100C)
step 4. water (100C) -> steam (100C)
step 5. steam (100C) -> steam (120C)
367500 kcal
Find the amount of heat energy needed to convert 150 grams of ice at -15°C to ice at -63°C.
To calculate the total amount of heat required to change 500g of ice at -10°C into 500g of steam at 120°C, we need to calculate the heat required for each step and then add them together.
Step 1: Ice (-10°C) to Ice (0°C)
The heat required to raise the temperature of ice without changing its phase can be calculated using the formula:
Q = m * c * ΔT
Where:
Q = heat required (in joules)
m = mass of the substance (in grams)
c = specific heat capacity of the substance (in J/g°C)
ΔT = change in temperature (in °C)
For ice:
m = 500g
c = 2.09 J/g°C (specific heat capacity of ice)
ΔT = 0°C - (-10°C) = 10°C
Q1 = 500g * 2.09 J/g°C * 10°C = 10,450 J
Step 2: Ice (0°C) to Water (0°C)
The heat required to change the ice at 0°C into water at 0°C can be calculated using the formula for heat of fusion:
Q2 = m * L_fusion
Where:
Q2 = heat required (in joules)
m = mass of the substance (in grams)
L_fusion = heat of fusion for ice (in J/g)
For ice:
m = 500g
L_fusion = 334 J/g (heat of fusion for ice)
Q2 = 500g * 334 J/g = 167,000 J
Step 3: Water (0°C) to Water (100°C)
The heat required to raise the temperature of water without changing its phase can be calculated using the formula:
Q3 = m * c * ΔT
Where:
Q3 = heat required (in joules)
m = mass of the substance (in grams)
c = specific heat capacity of the substance (in J/g°C)
ΔT = change in temperature (in °C)
For water:
m = 500g
c = 4.18 J/g°C (specific heat capacity of water)
ΔT = 100°C - 0°C = 100°C
Q3 = 500g * 4.18 J/g°C * 100°C = 209,000 J
Step 4: Water (100°C) to Steam (100°C)
The heat required to change the water at 100°C into steam at 100°C can be calculated using the formula for heat of vaporization:
Q4 = m * L_vaporization
Where:
Q4 = heat required (in joules)
m = mass of the substance (in grams)
L_vaporization = heat of vaporization for water (in J/g)
For water:
m = 500g
L_vaporization = 2260 J/g (heat of vaporization for water)
Q4 = 500g * 2260 J/g = 1,130,000 J
Step 5: Steam (100°C) to Steam (120°C)
The heat required to raise the temperature of steam without changing its phase can be calculated using the formula:
Q5 = m * c * ΔT
Where:
Q5 = heat required (in joules)
m = mass of the substance (in grams)
c = specific heat capacity of the substance (in J/g°C)
ΔT = change in temperature (in °C)
For steam:
m = 500g
c = 2.03 J/g°C (specific heat capacity of steam)
ΔT = 120°C - 100°C = 20°C
Q5 = 500g * 2.03 J/g°C * 20°C = 20,300 J
Total heat required:
Total Q = Q1 + Q2 + Q3 + Q4 + Q5
Total Q = 10,450 J + 167,000 J + 209,000 J + 1,130,000 J + 20,300 J
Total Q = 1,537,750 J
Therefore, the total amount of heat required to change 500g of ice at -10°C into 500g of steam at 120°C is 1,537,750 joules.
To calculate the total amount of heat needed to go from 500g of ice at -10°C to 500g of steam at 120°C, we need to calculate the heat required for each of the given steps and then add up the values.
Step 1: Ice (-10°C) to Ice (0°C)
The heat required to raise the temperature of ice from -10°C to 0°C is given by the formula:
Q = m * c * ΔT, where Q is the heat, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
The specific heat capacity of ice is approximately 2.09 J/g°C.
So, for Step 1, the heat required is:
Q1 = 500g * 2.09 J/g°C * (0°C - (-10°C))
Step 2: Ice (0°C) to Water (0°C)
The heat required to melt ice at 0°C to water at 0°C is given by:
Q = m * ΔHfusion, where ΔHfusion is the heat of fusion.
The heat of fusion for water is approximately 334 J/g.
So, for Step 2, the heat required is:
Q2 = 500g * 334 J/g
Step 3: Water (0°C) to Water (100°C)
The heat required to raise the temperature of water from 0°C to 100°C is given by:
Q = m * c * ΔT, where c is the specific heat capacity of water (4.18 J/g°C).
So, for Step 3, the heat required is:
Q3 = 500g * 4.18 J/g°C * (100°C - 0°C)
Step 4: Water (100°C) to Steam (100°C)
The heat required for converting water at 100°C to steam at 100°C (without changing its temperature) is given by the formula:
Q = m * ΔHvaporization, where ΔHvaporization is the heat of vaporization.
The heat of vaporization for water is approximately 2260 J/g.
So, for Step 4, the heat required is:
Q4 = 500g * 2260 J/g
Step 5: Steam (100°C) to Steam (120°C)
The heat required to raise the temperature of steam from 100°C to 120°C is given by:
Q = m * c * ΔT, where c is the specific heat capacity of steam (2.03 J/g°C).
So, for Step 5, the heat required is:
Q5 = 500g * 2.03 J/g°C * (120°C - 100°C)
To find the total amount of heat required, we add up all the individual steps:
Total heat required = Q1 + Q2 + Q3 + Q4 + Q5
Calculating the values for each step will give you the total heat required to change 500g of ice at -10°C into 500g of steam at 120°C.