A glass of ice water was made by adding six 25 g ice cubes to one liter of water. If the water was initially 25C and the ice cubes were initially at -15C, what is the final temperature of the ice water?
heat absorbed moving ice from -15 to zero + heat absorbed by ice melting + heat absorbed by moving ice from zero to final T - heat lost by 1L water initially at 25 C = 0.
[mass ice x specific heat ice x (Tfinal-Tinitial)] + [mass ice x heat fusion] + [mass melted ice x specific heat water x (Tfinal-Tinitial)] + [mass water x specific heat water x (Tfinal-Tinitial)] = 0
Solve for Tfinal.
To find the final temperature of the ice water, we can use the principle of conservation of energy. The total amount of energy before and after the ice cubes melt should be the same.
First, let's calculate the initial energy of the ice cubes. The specific heat capacity of ice is 2.09 J/g°C. Since the ice cubes are initially at -15°C and their mass is 25 g each, the initial energy of the ice cubes can be calculated as follows:
Initial energy of ice cubes = mass of each ice cube × specific heat capacity of ice × temperature change
= 25 g × 2.09 J/g°C × (0°C - (-15°C))
= 25 g × 2.09 J/g°C × 15°C
= 782.25 J
Next, let's calculate the energy required to heat the water. The specific heat capacity of water is 4.18 J/g°C. The mass of one liter of water is 1000 g. The temperature change required is the final temperature of the ice water minus the initial temperature of the water. Therefore, the energy required to heat the water is:
Energy required to heat water = mass of water × specific heat capacity of water × temperature change
= 1000 g × 4.18 J/g°C × (final temperature - 25°C)
Finally, as per the principle of conservation of energy, the initial energy of the ice cubes should be equal to the energy required to heat the water. Therefore, we can equate the two expressions:
782.25 J = 1000 g × 4.18 J/g°C × (final temperature - 25°C)
Simplifying the equation, we find:
782.25 J = 4180 J/°C × (final temperature - 25°C)
Dividing both sides of the equation by 4180 J/°C, we get:
(782.25 J) / (4180 J/°C) = final temperature - 25°C
Solving for the final temperature, we find:
final temperature = (782.25 J) / (4180 J/°C) + 25°C
final temperature ≈ 0.187°C + 25°C ≈ 25.187°C
Therefore, the final temperature of the ice water is approximately 25.187°C.