How many kilojoules of energy are needed to convert 104 g of ice at -14.6 to water at 25.8°C? (The specific heat of ice at -14.6 is 2.01 J/g°C.)
To find the energy needed to convert ice to water, we need to consider two steps:
Step 1: Heating the ice from -14.6°C to 0°C
Step 2: Melting the ice at 0°C to water at 25.8°C
Step 1: Heating the ice from -14.6°C to 0°C:
We will use the formula:
q1 = m * c * ΔT
Where:
q1 is the energy required,
m is the mass of the ice (104g),
c is the specific heat of ice at -14.6°C (2.01 J/g°C),
ΔT is the change in temperature (0°C - (-14.6°C)).
Substituting the values, we get:
q1 = 104g * 2.01 J/g°C * (0°C - (-14.6°C))
q1 = 104g * 2.01 J/g°C * 14.6°C
q1 ≈ 3027 J
Step 2: Melting the ice at 0°C to water at 25.8°C:
We need to account for the energy required to melt the ice at 0°C. The heat of fusion for ice is 334 J/g. We can calculate the energy needed using the formula:
q2 = m * ΔHf
Where:
q2 is the energy required,
m is the mass of the ice (104g),
ΔHf is the heat of fusion (334 J/g).
Substituting the values, we get:
q2 = 104g * 334 J/g
q2 ≈ 34,736 J
The total energy needed is the sum of q1 and q2:
Total energy = q1 + q2
Total energy ≈ 3027 J + 34,736 J
Total energy ≈ 37,763 J
Therefore, approximately 37,763 joules (or 37.8 kilojoules) of energy are needed to convert 104 g of ice at -14.6°C to water at 25.8°C.
To find the amount of energy required to convert ice at -14.6°C to water at 25.8°C, we need to consider two processes:
1. First, we need to heat the ice from -14.6°C to its melting point at 0°C.
2. Then, we need to convert the ice at 0°C to water at 25.8°C.
Let's break down the calculation step by step:
Step 1: Calculate the energy required to heat the ice from -14.6°C to 0°C.
The specific heat capacity (C) is given: 2.01 J/g°C
The mass (m) of ice is given: 104 g
The temperature change (Δt) is: 0 - (-14.6) = 14.6°C
To calculate the energy (Q) required, we can use the formula:
Q = m * C * Δt
Substituting the given values into the formula:
Q = 104 g * 2.01 J/g°C * 14.6°C
Step 2: Calculate the energy required to convert the ice at 0°C to water at 25.8°C.
For this process, we need to consider the heat of fusion (ΔHf) for ice, which is 333.5 J/g. This is the amount of energy required to convert ice at 0°C to water at 0°C.
The mass (m) of ice is given: 104 g
To calculate the energy (Q) required, we can use the formula:
Q = m * ΔHf
Substituting the given values into the formula:
Q = 104 g * 333.5 J/g
Now, let's calculate the total energy required by summing up the energy from both steps:
Total energy = Q1 + Q2
Total energy = (104 g * 2.01 J/g°C * 14.6°C) + (104 g * 333.5 J/g)
Calculating this expression will give you the required amount of energy in joules. To convert it to kilojoules, divide the answer by 1000.