Final Temperature After Phase Change and Transfer of Energy

In summary, the question asks for the final temperature of soup after adding a 0.011 kg cube of ice at 0 degrees Celsius to 0.450 kg of soup at 80.0 degrees Celsius, assuming the soup has the same specific heat capacity as water. Using the equations Q=mL and Q=ms(Tf-Ti), where Q is the heat transferred, m is the mass, L is the latent heat, s is the specific heat capacity, and Tf and Ti are the final and initial temperatures, the final temperature of the soup can be calculated by finding the heat needed to convert all ice to water and then finding the resulting temperature of the mixture of water and soup.
  • #1
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Homework Statement



A 0.011 kg cube of ice at 0.0 degrees Celsius is added to 0.450 kg of soup at 80.0 degrees Celsius. Assuming that the soup has the same specific heat capacity as water, find the final temperature of the soup after the ice has melted. (Hint: There is a temperature change after the ice melts.)

Specific heat capacity of ice: 2.09 x 10^3 J/(kg x degrees Celsius)

Specific heat capacity of water: 4.186 x 10^3 J/(kg x degrees Celsius)

Melting point of water: 0.0 degrees Celsius

Latent heat of fusion of water at standard pressure: 3.33 x 10^5 J/kg

answer: approximately 76.2 degrees Celscius

Homework Equations



Q = m x L
energy transferred as heat during a phase change = mass x latent heat

Q = m Cp deltaT
energy transferred as heat = mass x specific heat capacity x change in temperature

The Attempt at a Solution



... Okay, basically, I tried a bunch of different combinations of Q (Just about everything possible, except for the correct way apparently).

The closest i got to the answer, was 77.11 degrees Celsius, but i am not sure if i arrived at this answer correctly or if it's close enough, because i also came up with 78 degrees Celsius a few times.

1. Substituted values for ice into the equation of Q = m x L
2. Substituted values far ice into the equation of Q = m x Cp x deltaT
3. Substituted values for ice water into the equation of Q = m x Cp x deltaT
4. Added (1.) and (2.) together and set their sum equal to negative (3.)

Could i just get a hint or some other sort of guidance as to how to go about solving this? I have another problem like this, but this one seems to be the simpler of the two.

Just let me know if there is any additional information needed.
 
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  • #2
First, find the heat needed to convert all ice to water , given by Q=mL. This heat will be taken from the soup. So find the change in temp. of soup by Q=ms(Tf-Ti) , where Tf and Ti are final and initial temperatures. (your Q in this eqn is -ve ), so that final temp is lower than initial temperature.
Now you have two liquids, water at 0 degrees and soup at temp Tf. Just calculate the resulting temperature (T_ff) by -:

[tex] $ M_{water} \times s \times (T_{ff} - 0 ) = M_{soup} \times s \times (T_f-T_{ff}) $ [/tex]
 
Last edited:
  • #3
thank you for your help.
 

1. What is meant by "final temperature" in regards to phase change and transfer of energy?

Final temperature refers to the temperature of a substance after it has undergone a phase change and energy has been transferred to or from it. This is the temperature at which the substance reaches equilibrium and all of the energy has been either absorbed or released.

2. How does the phase change affect the final temperature of a substance?

The phase change of a substance can significantly impact its final temperature. For example, during a phase change from a solid to a liquid, the temperature will remain constant until the phase change is complete. This is because the energy being transferred is being used to break the intermolecular bonds, rather than raise the temperature. On the other hand, during a phase change from a liquid to a gas, the temperature will continue to rise until the phase change is complete.

3. What factors can affect the final temperature of a substance during a phase change?

The final temperature of a substance during a phase change can be influenced by a variety of factors. These include the initial temperature of the substance, the amount of energy being transferred, the specific heat capacity of the substance, and the strength of the intermolecular forces between the particles.

4. How is energy transferred during a phase change?

Energy is transferred during a phase change through the breaking or formation of intermolecular bonds between the particles of a substance. When energy is transferred to a substance, the bonds are broken and the particles gain energy, which can result in a phase change. When energy is transferred away from a substance, the bonds are formed and the particles lose energy, causing a phase change.

5. Can the final temperature after a phase change be predicted?

The final temperature after a phase change can be calculated using the equation Q = m * ΔH, where Q is the energy transferred, m is the mass of the substance, and ΔH is the heat of fusion or vaporization. However, this calculation assumes that the substance is in a closed system and no energy is lost to the surroundings. In reality, there may be other factors that can affect the final temperature, making it difficult to accurately predict.

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