How much heat energy is needed to change 3g of
ice at 0C to steam at 100C(Specific latent heat of
fusion of ice=336kj/kg, specific latent of
vapourization of water=2260kj/kg, specific heat
capacity of water=4.2kj/kgk)?
Do it for 1 kilogram first, then multiply by 0.003
1. melt the ice
heat in = 336 kJ
2. raise temp of water from 0 to 100
heat in = 100 (4.2 kJ/degK) = 420 kJ
3. boil it
heat in = 2260 kJ
add
3016 kJoules for 1 kg
multiply by 0.003
9.05 kJoules = 9050 Joules
To calculate the heat energy needed to change the ice at 0°C to steam at 100°C, we need to consider the different stages of the process:
1. Heating the ice from -10°C to 0°C:
First, we need to calculate the heat energy required to raise the temperature of 3g of ice from -10°C to 0°C, using the specific heat capacity of ice:
Q1 = mass × specific heat capacity × temperature difference
= 3g × 2.1 kJ/kg°C × (0°C - (-10°C))
= 3g × 2.1 kJ/kg°C × 10°C
= 63 J
2. Melting the ice at 0°C to water at 0°C:
Next, we need to calculate the heat energy required to melt the ice at 0°C to water at 0°C, using the specific latent heat of fusion of ice:
Q2 = mass × specific latent heat of fusion
= 3g × 336 kJ/kg
= 0.003 kg × 336 kJ/kg
= 1.008 kJ
3. Heating the water from 0°C to 100°C:
Then, we need to calculate the heat energy required to raise the temperature of the water from 0°C to 100°C, using the specific heat capacity of water:
Q3 = mass × specific heat capacity × temperature difference
= 3g × 4.2 kJ/kg°C × (100°C - 0°C)
= 3g × 4.2 kJ/kg°C × 100°C
= 1260 J
4. Vaporizing the water at 100°C to steam at 100°C:
Finally, we need to calculate the heat energy required to vaporize the water at 100°C to steam at 100°C, using the specific latent heat of vaporization of water:
Q4 = mass × specific latent heat of vaporization
= 3g × 2260 kJ/kg
= 0.003 kg × 2260 kJ/kg
= 6.78 kJ
Total heat energy required:
Q_total = Q1 + Q2 + Q3 + Q4
= 63 J + 1.008 kJ + 1260 J + 6.78 kJ
= 7881 J + 1.008 kJ
≈ 7.881 kJ
Therefore, approximately 7.881 kJ of heat energy is needed to change 3g of ice at 0°C to steam at 100°C.
To determine the amount of heat energy required to change the state of a substance, we need to consider the different stages and calculate the energy needed for each.
1. Heat energy to raise the temperature of the ice from -273.15°C to 0°C:
First, we need to calculate the heat energy required to raise the temperature of the ice. The specific heat capacity of water is given as 4.2 kJ/kgK. Since the ice is at -273.15°C, we need to raise its temperature by 273.15°C to reach 0°C.
The mass of ice is given as 3 grams, which is equivalent to 0.003 kg.
The formula to calculate the heat energy required is:
Q = mass * specific heat capacity * temperature change
Q = 0.003 kg * 4.2 kJ/kgK * 273.15 K
Q = 34.2594 kJ
Therefore, the heat energy required to raise the temperature of the ice from -273.15°C to 0°C is approximately 34.26 kJ.
2. Heat energy to melt the ice at 0°C:
The specific latent heat of fusion of ice is given as 336 kJ/kg. This means that for every kilogram of ice, 336 kJ of energy is needed to change it from solid to liquid at its melting point.
Since the mass of ice is 0.003 kg, we can calculate the heat energy required to melt the ice:
Q = mass * specific latent heat of fusion
Q = 0.003 kg * 336 kJ/kg
Q = 1.008 kJ
Therefore, the heat energy required to melt the ice at 0°C is approximately 1.01 kJ.
3. Heat energy to raise the temperature of the water from 0°C to 100°C:
After the ice has melted, we need to calculate the heat energy required to raise the temperature of the water from 0°C to 100°C.
The mass of water remains the same as the mass of ice, which is 0.003 kg.
The formula to calculate the heat energy required is the same as in the first step:
Q = mass * specific heat capacity * temperature change
Q = 0.003 kg * 4.2 kJ/kgK * 100 K
Q = 1.26 kJ
Therefore, the heat energy required to raise the temperature of the water from 0°C to 100°C is approximately 1.26 kJ.
4. Heat energy to vaporize the water at 100°C:
The specific latent heat of vaporization of water is given as 2260 kJ/kg. This means that for every kilogram of water, 2260 kJ of energy is needed to change it from liquid to gas at its boiling point.
Since the mass of water is 0.003 kg, we can calculate the heat energy required to vaporize the water:
Q = mass * specific latent heat of vaporization
Q = 0.003 kg * 2260 kJ/kg
Q = 6.78 kJ
Therefore, the heat energy required to vaporize the water at 100°C is approximately 6.78 kJ.
Finally, to find the total heat energy required, we add up the energy values calculated in each step:
Total heat energy = heat energy to raise temperature of ice + heat energy to melt ice + heat energy to raise temperature of water + heat energy to vaporize water
Total heat energy = 34.26 kJ + 1.01 kJ + 1.26 kJ + 6.78 kJ
Total heat energy = 43.31 kJ
Therefore, approximately 43.31 kJ of heat energy is needed to change 3 g of ice at 0°C to steam at 100°C.