Heat and Phase : Latent heat

In summary, the problem asked for the final temperature of 160 cm^3 of coffee at 82.7 °C after two 10.0-g ice cubes at 0 °C completely melt inside the thermos. The equation Q=mL was used to find the change in energy required to melt the ice cubes. The mass and density of water were needed to find the change in temperature of the coffee. The final temperature was found by calculating the amount of energy that needed to be traded from the hot water to the cold water for their temperatures to be equal.
  • #1
salooom599
4
0

Homework Statement


A thermos contains 160 cm^3 of coffee at 82.7 °C. To cool the coffee, you drop two 10.0-g ice cubes into the thermos. The ice cubes are initially at 0 °C and melt completely. What is the final temperature of the coffee in degrees Celsius? Treat the coffee as if it were water.

Homework Equations



Q=mL
mL=Cm(T final-T initial )

The Attempt at a Solution


i really don't know how to slove it and why there is 160 cm^3
 
Last edited:
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  • #2
Hey Salooom, Welcome to PF.
Do you have a table giving the specific latent heat (etc.) of water?
It seems that firstly you need to find the change energy required to melt the ice cubes, and the change in temperature this would cause in the coffee.
Now I'm not particularly fresh in this field, but it seems to me that you need to know the total mass of the water, do you have a value for the density of water?

Then you have some amount of water at 0*C, and some amount at a higher temperature (The original temp - the amount of heat needed to melt the cubes), and you simply work out at how much energy needs to be traded from the hot water to the cold waterfor their temperatures to be the same.
 
  • #3
ok i got it :D
thankss..
 
  • #4
salooom599 said:
ok i got it :D
thankss..

No problem. Glad I could help (for once!) :wink:
 
  • #5


I would approach this problem by first understanding the concepts of heat and phase and how they relate to each other. Heat is a form of energy that can cause a change in temperature or phase of a substance. Phase refers to the physical state of a substance, such as solid, liquid, or gas.

In this problem, we are dealing with the process of cooling the coffee, which involves a change in phase from liquid to solid for the ice cubes. This change in phase requires a specific amount of energy, known as latent heat, which is given by the equation Q=mL, where Q is the amount of energy, m is the mass of the substance, and L is the latent heat of the substance.

We are also given the initial temperature of the coffee, 82.7 °C, and the final temperature, which we need to calculate. To do this, we can use the equation mL=Cm(T final-T initial ), where Cm is the specific heat capacity of the substance. In this case, we can treat the coffee as if it were water, so we can use the specific heat capacity of water, which is 4.18 J/g°C.

Now, let's look at the given information. We are told that the thermos contains 160 cm^3 of coffee, which is the volume of the coffee. This information is important because it helps us determine the mass of the coffee, which is needed to calculate the latent heat. We know that the density of water is 1 g/cm^3, so the mass of the coffee is 160 g.

Next, we are told that two 10.0-g ice cubes are dropped into the thermos. This means that the total mass of the ice cubes is 20 g. We also know that the initial temperature of the ice cubes is 0 °C, and they melt completely, which means they absorb a specific amount of energy to change from solid to liquid.

Putting all of this information together, we can set up the following equation to solve for the final temperature of the coffee:

(20 g)(334 J/g) + (160 g)(4.18 J/g°C)(T final - 82.7 °C) = 0

Solving for T final, we get a final temperature of 26.2 °C. This makes sense because the ice cubes will absorb a large amount of energy to melt, which will cause a decrease in the
 

1. What is heat?

Heat is a form of energy that is transferred between objects or systems due to a temperature difference. It is commonly measured in units of joules (J) or calories (cal).

2. What is phase change?

Phase change refers to the process of a substance changing from one physical state to another, such as from solid to liquid or liquid to gas. This process often involves the absorption or release of heat energy.

3. What is latent heat?

Latent heat is the amount of heat energy required to change the phase of a substance without changing its temperature. This energy is used to break the intermolecular bonds holding the molecules together.

4. How is latent heat related to phase change?

During a phase change, the temperature of a substance remains constant as heat energy is absorbed or released to break or form new intermolecular bonds. This energy is known as latent heat.

5. How does the heat of fusion differ from the heat of vaporization?

The heat of fusion is the amount of heat energy required to change a substance from solid to liquid, while the heat of vaporization is the amount of heat energy required to change a substance from liquid to gas. Both involve a phase change and the absorption or release of latent heat.

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