Final temperature of the liquid water?

In summary, The final temperature of the liquid water can be found by setting up an energy balance equation, where the heat absorbed is equal to the heat required to change the phase of the ice and increase the temperature of the water. Using the equation Q=mcT+mL, the correct answer can be found by considering the heat gained from melting the ice and warming up the water.
  • #1
name_ask17
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Homework Statement


A 10-kg block of ice has a temperature of -12°C. The pressure is one atmosphere. The block absorbs 4.15 106J of heat. What is the final temperature of the liquid water?



Homework Equations


Q=mcT



The Attempt at a Solution


i know i have to find the change from -12 to 0 deg c and then use mLfusion for the ice and add them. i am lost after that. i keep getting the wrong answer. how do i do this?
 
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  • #2


name_ask17 said:

The Attempt at a Solution


i know i have to find the change from -12 to 0 deg c and then use mLfusion for the ice and add them. i am lost after that. i keep getting the wrong answer. how do i do this?

You'll need to do an energy balance.

Heat absorbed = heat to change phase of the ice + heat to increase the temperature from -12 to T.

you know that heat to change phase of the ice=mLfusion and the heat to increase the temperature = mc(T2-T1).
 
  • #3


so would i do Q=mcT+mL as 4.15E6=(10)(4186)(T-12)+(10)(334)? because that is not giving me the correct answer. can you please explain to me what I am doing wrong here?
 
  • #4


dont bother. i undersand it now. i was to take the heat gained to ive, ice melting, and water warming up. thank you for your assistance
 
  • #5


I would approach this problem by first identifying the known values and the unknown value. In this case, we know the mass of the ice (10 kg), its initial temperature (-12°C), and the amount of heat absorbed (4.15 x 10^6 J). The unknown value is the final temperature of the liquid water.

Next, I would use the equation Q=mcT to calculate the change in temperature of the ice. We know the specific heat capacity of ice (c) is 2.1 J/g°C and the mass (m) is 10 kg, so we can plug in these values to solve for the change in temperature (T).

Q = (10 kg)(2.1 J/g°C)(T - (-12°C))

4.15 x 10^6 J = (10 kg)(2.1 J/g°C)(T + 12°C)

T + 12°C = 1976190.48

T = 1976190.48 - 12°C

T = 1976178.48°C

This is the change in temperature of the ice. To find the final temperature of the liquid water, we need to add this change to the initial temperature of the ice.

Final temperature = -12°C + 1976178.48°C = 1976166.48°C

However, this answer is not realistic as it is well above the boiling point of water. This indicates that the ice has not completely melted and there may be some error in the calculations.

To find the final temperature more accurately, we need to take into account the latent heat of fusion for ice, which is the energy required to melt the ice without changing its temperature. This can be calculated using the equation Q=mLfusion, where m is the mass of the ice and Lfusion is the latent heat of fusion for ice (334 kJ/kg).

Q = (10 kg)(334 kJ/kg)

Q = 3340 kJ

Now, we can subtract this amount of energy from the total heat absorbed to find the remaining energy that will be used to increase the temperature of the liquid water.

Remaining energy = 4.15 x 10^6 J - 3340 kJ = 4.14666 x 10^6 J

Using the equation Q=mcT, we can now solve for the final temperature of the liquid water.

4.14666 x 10
 

1. What factors affect the final temperature of liquid water?

The final temperature of liquid water is affected by several factors such as the initial temperature of the water, the amount of heat applied, the type of container the water is in, and the surrounding environment.

2. How is the final temperature of liquid water calculated?

The final temperature of liquid water can be calculated using the formula: Tf = (m1 x T1 + m2 x T2) / (m1 + m2), where Tf is the final temperature, m1 and m2 are the masses of the water and the container, and T1 and T2 are the initial temperatures of the water and the container, respectively.

3. Does the final temperature of liquid water change with the amount of water?

Yes, the final temperature of liquid water can change with the amount of water. This is because a larger amount of water requires more heat to raise its temperature compared to a smaller amount of water.

4. Can the final temperature of liquid water exceed 100 degrees Celsius?

Yes, the final temperature of liquid water can exceed 100 degrees Celsius. This is known as superheating and can occur when the water is heated in a clean container without any impurities or when it is heated in a microwave.

5. How does the surrounding environment affect the final temperature of liquid water?

The surrounding environment can greatly impact the final temperature of liquid water. For example, in a colder environment, the water will cool down more quickly, resulting in a lower final temperature. On the other hand, in a warmer environment, the water will retain its heat for a longer period of time, resulting in a higher final temperature.

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