What is the final temperature, in oC, after a 15.0 g piece of ice, at 0oC, is placed in a styrofoam cup with 128 g of water initially at 74.0oC.
Assume there is no transfer of heat to or from the surroundings.
The specific heat of water = 4.184 JK-1g-1
The heat of fusion of ice = 333 Jg-1
heat added to ice to melt it + heat added to melt at zero C to final T + heat lost by hot water = 0
heat added to ice to melt it is mass ice x heat fusion.
heat added to melt at zero to final T is
mass melt x specific heat water x (Tfinal-Tinitial)
heat lost by hot water is
mass x specific heat x (Tfinal-Tinitial).
Set the sum of these to zero and solve for Tf.
To find the final temperature after mixing ice and water, we need to use the principles of heat transfer and energy conservation.
1. First, calculate the heat gained by the ice to reach its melting point:
- Mass of ice (m1) = 15.0 g
- Heat gained by ice = (mass of ice) x (heat of fusion of ice)
- Heat gained by ice = 15.0 g x 333 J/g
2. Next, calculate the heat gained by the water to reach the same temperature:
- Mass of water (m2) = 128 g
- Initial temperature of water (T2i) = 74.0 °C
- Final temperature of water and ice mixture (Tf)
- Heat gained by water = (mass of water) x (specific heat of water) x (Tf - T2i)
3. Since there is no transfer of heat to or from the surroundings, the total heat gained by the system (ice + water) must be equal to zero:
- Total heat gained = Heat gained by ice + Heat gained by water
- 0 = (mass of ice) x (heat of fusion of ice) + (mass of water) x (specific heat of water) x (Tf - T2i)
4. Rearrange the equation to solve for the final temperature (Tf):
- Tf = [((mass of ice) x (heat of fusion of ice)) / ((mass of water) x (specific heat of water))] + T2i
Now, plug in the given values and calculate Tf:
Tf = [(15.0 g x 333 J/g) / (128 g x 4.184 J/g°C)] + 74.0 °C
Tf ≈ 14.67 °C
Therefore, the final temperature after mixing the ice and water is approximately 14.67 °C.