If 135 g of ice at 0.0°C is added to 2.96 L of water at 85°C, what is the final temperature of the mixture?
the sum of the heats gained is zero.
heatmeltingcice+ heatheating water=0
.135*Hf+2.96*specificheatwater*(Tf-85)=0
notice I used masses in kg, so your heat of fusion needs to be in units of kj/kg, and specific heat needs to be in kJ/kg-C
To find the final temperature of the mixture, we can use the principle of conservation of energy. The heat lost by the hot water (water at 85°C) will be equal to the heat gained by the cold ice (ice at 0.0°C). The equation used for this calculation is:
Q_lost = Q_gained
Where Q_lost is the heat lost by the hot water, Q_gained is the heat gained by the ice, and they are both measured in joules.
To calculate the heat lost by the hot water, we can use the formula:
Q_lost = mass_water * specific_heat_water * change_in_temperature_water
Where mass_water is the mass of water, specific_heat_water is the specific heat capacity of water, and change_in_temperature_water is the change in temperature of the water (final temperature - initial temperature).
To calculate the heat gained by the ice, we can use the formula:
Q_gained = mass_ice * specific_heat_ice * change_in_temperature_ice
Where mass_ice is the mass of the ice, specific_heat_ice is the specific heat capacity of ice, and change_in_temperature_ice is the change in temperature of the ice (final temperature - initial temperature).
After determining the heat lost by the hot water and the heat gained by the ice, we can set up the equation:
mass_water * specific_heat_water * change_in_temperature_water = mass_ice * specific_heat_ice * change_in_temperature_ice
We know the mass of the ice (135 g), the mass of the water (2.96 L), the specific heat capacity of water (4.18 J/g°C), and the specific heat capacity of ice (2.09 J/g°C).
Let's proceed with the calculations:
1. Convert the volume of water from liters to grams:
- The density of water is 1 g/mL.
- Therefore, 2.96 L = 2.96 * 1000 g = 2960 g.
2. Calculate the heat lost by the water:
- mass_water = 2960 g
- specific_heat_water = 4.18 J/g°C
- change_in_temperature_water = final_temperature - initial_temperature = final_temperature - 85°C
- Q_lost = mass_water * specific_heat_water * change_in_temperature_water
3. Calculate the heat gained by the ice:
- mass_ice = 135 g
- specific_heat_ice = 2.09 J/g°C
- change_in_temperature_ice = final_temperature - initial_temperature = final_temperature - 0.0°C
- Q_gained = mass_ice * specific_heat_ice * change_in_temperature_ice
4. Set up the equation and solve for the final temperature:
- mass_water * specific_heat_water * change_in_temperature_water = mass_ice * specific_heat_ice * change_in_temperature_ice
- 2960 g * 4.18 J/g°C * (final_temperature - 85°C) = 135 g * 2.09 J/g°C * (final_temperature - 0.0°C)
Solve the equation for the final temperature to find the answer.