A 10 kg block of ice has a temperature of -13°C. The pressure is one atmosphere. The block absorbs 4.11 106 J of heat. What is the final temperature of the liquid water?
To find the final temperature of the liquid water, we need to use the formula for the specific heat capacity. The specific heat capacity of ice is 2.09 J/g°C and the specific heat capacity of water is 4.18 J/g°C.
First, we need to calculate the heat required to raise the temperature of the ice from -13°C to 0°C. The formula to calculate the heat energy is Q = m * c * ∆T, where Q is the heat energy, m is the mass, c is the specific heat capacity, and ∆T is the change in temperature.
Q = (10 kg) * (2.09 J/g°C) * (0°C - (-13°C))
Q = (10,000 g) * (2.09 J/g°C) * (13°C)
Q = 270,700 J
Next, we need to calculate the heat required to melt the ice into water. The formula to calculate the heat energy for phase change is Q = m * Lf, where Lf is the latent heat of fusion.
Q = (10 kg) * (334 J/g)
Q = (10,000 g) * (334 J/g)
Q = 3,340,000 J
Now, we need to calculate the heat required to raise the temperature of the water from 0°C to the final temperature. We can use the same formula as before.
Q = (10 kg) * (4.18 J/g°C) * (∆T)
Substituting the known values, we have:
4.11 x 10^6 J = (10,000 g) * (4.18 J/g°C) * (∆T)
Simplifying the equation, we have:
∆T = (4.11 x 10^6 J) / (10,000 g * 4.18 J/g°C)
∆T ≈ 98.56°C
Finally, to find the final temperature, we add the change in temperature (∆T) to the initial temperature of 0°C:
Final temperature = 0°C + 98.56°C
Final temperature ≈ 98.56°C
Therefore, the final temperature of the liquid water is approximately 98.56°C.