How much heat is necessary to change 305g of ice at -11c to water at 20c
heat the ice to 0º
melt the ice
heat the water to 20º
look up the heat of fusion for ice
and the specific heats for ice and water
To calculate the amount of heat required to change a substance from one state to another, you need to consider the specific heat capacity and the phase change enthalpy of the substance.
In this case, we need to calculate the heat required to change ice at -11°C to water at 20°C. Let's break it down into several steps:
1. Heating the ice from -11°C to 0°C:
- The specific heat capacity of ice is 2.09 J/g°C.
- The temperature change is 0°C - (-11°C) = 11°C.
- The heat required for this step can be calculated as:
Heat_1 = mass * specific heat capacity * temperature change
= 305g * 2.09 J/g°C * 11°C
2. Melting the ice at 0°C:
- The heat of fusion (also known as latent heat) of ice is 334 J/g.
- The mass of the ice that needs to be melted is still 305g.
- The heat required for this step can be calculated as:
Heat_2 = mass * heat of fusion
= 305g * 334 J/g
3. Heating the melted ice from 0°C to 20°C:
- The specific heat capacity of water is 4.18 J/g°C.
- The temperature change is 20°C - 0°C = 20°C.
- The mass of the water is still 305g.
- The heat required for this step can be calculated as:
Heat_3 = mass * specific heat capacity * temperature change
= 305g * 4.18 J/g°C * 20°C
Total heat required:
Total_heat = Heat_1 + Heat_2 + Heat_3
Now, you can substitute the values and calculate the total heat required.
To determine the amount of heat necessary to change ice at -11°C to water at 20°C, we need to consider the different phase changes and temperature ranges involved.
First, we need to calculate the heat required to raise the temperature of the ice from -11°C to 0°C, where it will start to melt. The specific heat capacity of ice is approximately 2.09 J/g°C.
Q1 = mass × specific heat capacity × change in temperature
= 305g × 2.09 J/g°C × (0 - (-11)°C)
= 305g × 2.09 J/g°C × 11°C
≈ 6727.95 J
Next, we need to calculate the heat required to melt the ice at 0°C into water at 0°C. The specific heat of fusion for ice is 334 J/g.
Q2 = mass × specific heat of fusion
= 305g × 334 J/g
≈ 101770 J
After all the ice has melted, we need to calculate the heat required to raise the temperature of the resulting water from 0°C to 20°C. The specific heat capacity of water is approximately 4.18 J/g°C.
Q3 = mass × specific heat capacity × change in temperature
= 305g × 4.18 J/g°C × (20 - 0)°C
= 305g × 4.18 J/g°C × 20°C
≈ 252194 J
Finally, we add up the three heat values to find the total amount of heat required:
Total Q = Q1 + Q2 + Q3
= 6727.95 J + 101770 J + 252194 J
≈ 360692 J
Therefore, approximately 360,692 Joules (J) of heat is necessary to change 305g of ice at -11°C to water at 20°C.