How much energy is required to convert 64.0 g of ice to water at 55.0 ℃
To calculate the energy required to convert ice to water at a specific temperature, we need to consider the following steps:
1. Determine the energy required to raise the temperature of the ice to its melting point.
2. Determine the energy required to convert the ice at its melting point to water at the same temperature.
Let's perform these calculations step by step:
Step 1: Determine the energy required to raise the temperature of the ice to its melting point.
The energy required to raise the temperature of a substance can be calculated using the formula:
Q1 = m * C * ΔT
Where:
Q1 is the energy required (in joules),
m is the mass of the substance (in grams),
C is the specific heat capacity of the substance (in J/g°C), and
ΔT is the change in temperature (in °C).
For ice, the specific heat capacity is typically around 2.09 J/g°C.
Using the given values:
m = 64.0 g
C = 2.09 J/g°C
ΔT = (0 °C - (-10 °C)) = 10 °C (since the melting point of ice is generally considered to be at 0 °C)
Q1 = 64.0 g * 2.09 J/g°C * 10 °C = 1337.6 J
Step 2: Determine the energy required to convert the ice at its melting point to water at the same temperature.
The energy required for phase change (heat of fusion) can be calculated using the formula:
Q2 = m * ΔHf
Where:
Q2 is the energy required (in joules),
m is the mass of the substance (in grams), and
ΔHf is the heat of fusion (in J/g).
The heat of fusion for ice is approximately 334 J/g.
Using the given value:
m = 64.0 g
ΔHf = 334 J/g
Q2 = 64.0 g * 334 J/g = 21376 J
Now, we can calculate the total energy required by summing up Q1 and Q2:
Total Energy = Q1 + Q2 = 1337.6 J + 21376 J = 22713.6 J
Therefore, approximately 22,713.6 joules of energy are required to convert 64.0 grams of ice to water at 55.0 °C.
To calculate the energy required to convert ice to water, we need to consider two processes: raising the temperature of the ice to its melting point, and then converting the ice at its melting point to water.
First, let's calculate the amount of energy required to raise the temperature of the ice to its melting point. The specific heat capacity of ice is 2.09 J/g°C. The temperature change is given by:
ΔT = Melting point temperature - initial temperature
= 0℃ - (-10℃)
= 10℃
The energy required is given by the equation:
q1 = mass × specific heat capacity × ΔT
q1 = 64.0 g × 2.09 J/g°C × 10℃
= 1,331.2 J
The energy required to convert the ice to water at its melting point is given by:
q2 = mass × heat of fusion
The heat of fusion for water is 334 J/g. So,
q2 = 64.0 g × 334 J/g
= 21,376 J
Finally, the total energy required is the sum of q1 and q2:
Total energy = q1 + q2
= 1,331.2 J + 21,376 J
= 22,707.2 J
Therefore, the energy required to convert 64.0 g of ice to water at 55.0℃ is 22,707.2 J.