What is the final temperature and physical state of water when 250 grams of water at 85 degrees C is added to 80.0 grams of ice at -15 degree C?
Is the physical state of water liquid?
I don't understand the set up.
The setup is like this (answered by bobpursly):
The sum of heats gained =0
80(cice)(0+15)+80Hf+80cw(Tf-0)+250cw(Tf-85)=0
solve for Tfinal Tf
what do you not understand? some lose heat (a negative heat gained) and some gain heat, the sum is zero.
To understand the setup for solving this problem, let's break it down step by step:
Step 1: Identify the given information.
We have:
- Mass of water (m1) = 250 grams
- Initial temperature of water (T1) = 85 degrees Celsius
- Mass of ice (m2) = 80.0 grams
- Initial temperature of ice (T2) = -15 degrees Celsius
Step 2: Identify the unknowns.
We need to find:
- The final temperature of the system (Tfinal)
- The physical state of water at the final temperature
Step 3: Apply the conservation of energy principle.
The principle of conservation of energy states that the total heat gained must equal the total heat lost.
Step 4: Determine the heat gained by the ice.
The heat gained by the ice can be calculated using the equation:
Q = m * c * ΔT
- Where Q is the heat gained or lost, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
The heat gained by the ice can be broken down into two parts:
- Heat gained to raise the temperature from -15°C to 0°C.
- Heat gained to melt the ice at 0°C.
Step 5: Determine the heat gained by the water.
Similar to the ice, the heat gained by the water can also be calculated using the equation Q = m * c * ΔT. However, since the water is changing from liquid to solid (ice), we need to account for the heat lost during this phase transition.
The heat gained by the water can be broken down into two parts:
- Heat gained to cool the water from 85°C to the final temperature.
- Heat lost during the freezing of the water at 0°C.
Step 6: Set up the equation for the conservation of energy.
To set up the equation, we sum up the heat gained and lost by the ice and water and set it equal to zero.
80(cice)(0+15) + 80Hf + 80cw(Tfinal - 0) + 250cw(Tfinal - 85) = 0
- Where Hf is the heat of fusion (heat required to change the phase from a solid to a liquid or vice versa).
- cw is the specific heat capacity of water.
Step 7: Solve the equation for the final temperature (Tfinal).
Rearrange the equation and solve for Tfinal.
Step 8: Determine the physical state of water at the final temperature.
If the final temperature (Tfinal) is above 0°C, the water will be in the liquid state. If the final temperature is below 0°C, the water will be in the solid state (ice).
In this case, since we found the value of Tfinal to solve the equation, you can evaluate whether the physical state of water is liquid by comparing it with the freezing point of water (0°C).