How much energy is required to change a 57 g ice cube from ice at −4◦C to steam at 107◦C? The specific heat of ice is 2090 J/kg ·◦ C and of water 4186 J/kg ·◦ C. The latent heat of fusion of water is 3.33 × 105 J/kg, its latent heat of vaporization is 2.26 × 106 J/kg, and the specific heat of steam is 2010 J/kg ·◦ C.
Answer in units of MJ
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20.65
To find the total energy required to change a 57 g ice cube from ice at -4°C to steam at 107°C, we need to calculate the energy required for each phase change and temperature change separately, and then sum them up.
Let's break down the process step by step:
1. First, we need to calculate the energy required to raise the temperature of the ice from -4°C to 0°C.
The specific heat capacity of ice is given as 2090 J/kg ·°C. Since we have 57 g of ice, we convert it to kilograms by dividing by 1000: 57 g = 0.057 kg.
The temperature change is 0°C - (-4°C) = 4°C.
Therefore, the energy required to raise the temperature of ice is: Energy = (mass) x (specific heat capacity) x (temperature change)
Energy = (0.057 kg) x (2090 J/kg ·°C) x (4°C)
2. Next, we need to calculate the energy required to melt the ice at 0°C into water at 0°C.
The latent heat of fusion of water is given as 3.33 × 105 J/kg.
Therefore, the energy required to change the ice to water is: Energy = (mass) x (latent heat of fusion)
Energy = (0.057 kg) x (3.33 × 105 J/kg)
3. Then, we need to calculate the energy required to raise the temperature of the water from 0°C to 100°C.
The specific heat capacity of water is given as 4186 J/kg ·°C.
The temperature change is 100°C - 0°C = 100°C.
Therefore, the energy required to raise the temperature of water is: Energy = (mass) x (specific heat capacity) x (temperature change)
Energy = (0.057 kg) x (4186 J/kg ·°C) x (100°C)
4. Now, we need to calculate the energy required to change the water at 100°C into steam at 100°C.
The latent heat of vaporization of water is given as 2.26 × 106 J/kg.
Therefore, the energy required to change water to steam is: Energy = (mass) x (latent heat of vaporization)
Energy = (0.057 kg) x (2.26 × 106 J/kg)
5. Finally, we need to calculate the energy required to raise the temperature of the steam from 100°C to 107°C.
The specific heat capacity of steam is given as 2010 J/kg ·°C.
The temperature change is 107°C - 100°C = 7°C.
Therefore, the energy required to raise the temperature of steam is: Energy = (mass) x (specific heat capacity) x (temperature change)
Energy = (0.057 kg) x (2010 J/kg ·°C) x (7°C)
To find the total energy required, we add up the energies calculated in each step:
Total energy required = Energy(step 1) + Energy(step 2) + Energy(step 3) + Energy(step 4) + Energy(step 5)
Finally, convert the total energy to megajoules (MJ) by dividing by 1,000,000.
I leave it to you to perform the calculations and provide the final answer in units of MJ.