25) A 75-g ice cube at 0 C is placed in 825g of water at 25 C. a) What is the final temperature of the mixture? b) If the final temperature is 0 C, then how much ice remains?
c) change the ice's mass to 300g, and repeat the problem
I don't know how to work this at all!!! PLEASE HELP!
How do you find the final temperature of the mixture though?
Sure! Let's work through the problem step by step:
a) To determine the final temperature of the mixture, we can use the principle of energy conservation. The amount of heat lost by the water (m1) is equal to the amount of heat gained by the ice (m2) during the temperature change:
m1 * c * ΔT1 = m2 * c * ΔT2
where:
m1 = mass of water = 825 g
ΔT1 = change in temperature of water = final temperature - initial temperature = final temperature - 25°C
m2 = mass of ice = 75 g
ΔT2 = change in temperature of ice = final temperature - initial temperature = final temperature - 0°C
c = specific heat capacity of water = 4.18 J/g°C (assuming for both water and ice)
We can rearrange the equation to solve for the final temperature:
final temperature = (m1 * c * ΔT1 + m2 * c * ΔT2) / (m1 * c + m2 * c)
Substituting the given values into the equation, we get:
final temperature = (825 * 4.18 * (final temperature - 25) + 75 * 4.18 * (final temperature - 0)) / (825 * 4.18 + 75 * 4.18)
Simplifying the equation:
(825 * 4.18 * final temperature - 825 * 4.18 * 25 + 75 * 4.18 * final temperature) / (825 * 4.18 + 75 * 4.18) = final temperature
Now, we can solve this equation to find the final temperature.
b) If the final temperature of the mixture is 0°C, then all of the ice has melted. This is because the final temperature reached is the melting point of ice, and any remaining ice would continue to absorb heat until it melts.
c) To repeat the problem with an ice mass of 300g, you would follow the same steps as in part a), but replace the mass of ice (m2) with 300g in the calculations.
I hope this helps! Let me know if you have any further questions.
No worries! I'm here to help you understand and solve this problem step by step.
Let's first tackle part a) of the question, which asks for the final temperature of the mixture.
To solve this, we need to use the principle of conservation of energy and apply the concept of heat transfer. The heat gained by the water should be equal to the heat lost by the ice.
Here's how you can calculate the final temperature of the mixture:
1. Determine the heat transfer from the water to the ice.
- Use the equation Q = m * c * ΔT, where Q is the heat transfer, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
- The specific heat capacity of water is approximately 4.18 J/g°C.
- Calculate the heat transfer for the water: Qwater = mwater * cwater * ΔTwater.
- mwater = 825 g, ΔTwater = (final temperature - initial temperature).
- The initial temperature of the water is 25°C.
2. Determine the heat transfer from the ice to melt it.
- To raise the ice's temperature from 0°C to its melting point (0°C), you need to use the equation Q = m * heat of fusion (ΔHf).
- The heat of fusion for water is approximately 334 J/g.
- Since there is only one substance (the ice) involved in this step, we can simply calculate the heat transfer: Qice = mice * ΔHf.
3. Equate the two heat transfers:
- Qwater = Qice.
- Substitute the values you calculated for Qwater and Qice.
- Solve the equation for the final temperature by isolating ΔTwater.
The final temperature you find will be the answer to part a) of the question.
Now let's move on to part b) of the question, which asks how much ice remains if the final temperature is 0°C.
To determine the mass of ice that remains, we need to calculate the heat transfer from the water to the ice as we did before. However, instead of solving for the final temperature, we will solve for the mass of the ice (mice) using the equation Qwater = mice * ΔHf.
Finally, let's address part c) of the question, which asks to change the ice's mass to 300g and repeat the problem.
To solve part c), simply re-calculate the final temperature and the mass of ice remaining using the new mass value of 300g instead of the original 75g.
I hope this explanation helps you understand how to approach and solve this problem! If you need further clarification or have any additional questions, feel free to ask.
Go through the numbers and you should find that there is enough energy in the water to melt all of the 75 g of ice, but not 300 g of ice.
In the 75 g case, after all the ice is melted, the remaining heat in the water gets transferred to the melted ice, resulting in a final temperature between 0 and 25 C.
In the second (300 g of ice) case, not all of the ice melts. Calculate how much heat is lost cooling the water to 0 C, and see how much of the ice can be melted in the process.