the mass of the water is 131 kg and its initial temperature is 24.2°C, how much energy must the water transfer to its surroundings in order to freeze completely? The specific heat of water is 4186 J/kg·K, and the latent heat of fusion is 333 kJ/kg
heat=mass*specificheat*(0-24.2)+Hf*mass
To calculate the amount of energy required for water to freeze completely, we can break it down into two steps:
Step 1: Calculate the energy required to cool the water from its initial temperature to the freezing point.
Step 2: Calculate the energy required to freeze the water at the freezing point.
Step 1:
The energy required to change the temperature of the water can be calculated using the formula:
Q1 = m * c * ΔT
Where:
Q1 is the energy required (in Joules),
m is the mass of the water (in kg),
c is the specific heat capacity of water (4186 J/kg·K), and
ΔT is the change in temperature (in Kelvin).
In this case, the water starts at 24.2°C and needs to be cooled down to the freezing point, which is 0°C.
ΔT = (0°C + 273.15) - (24.2°C + 273.15)
Calculating the value of ΔT:
ΔT = (273.15 - 24.2)
ΔT = 248.95 Kelvin
Now, substitute the values into the equation to calculate Q1:
Q1 = 131 kg * 4186 J/kg·K * 248.95 K
Calculating the value of Q1:
Q1 = 137,628,622.9 J (Joules)
Step 2:
The energy required to freeze the water can be calculated using the formula:
Q2 = m * Lf
Where:
Q2 is the energy required (in Joules),
m is the mass of the water (in kg),
Lf is the latent heat of fusion of water (333,000 J/kg).
Substitute the values into the equation to calculate Q2:
Q2 = 131 kg * 333,000 J/kg
Calculating the value of Q2:
Q2 = 43,623,000 J (Joules)
Finally, to get the total energy required for water to freeze completely, add Q1 and Q2 together:
Total Energy = Q1 + Q2
Calculating the value of Total Energy:
Total Energy = 137,628,622.9 J + 43,623,000 J
Total Energy = 181,251,622.9 J (Joules)
Therefore, the water must transfer 181,251,622.9 Joules of energy to its surroundings in order to freeze completely.