# Heat and Internal Energy - Thermodynamics

• Marcin H
In summary, when dealing with a problem involving phase changes, you must take into account the latent heat of the substance and pay attention to the sign of the change. The latent heat can be looked up for substances like water.
Marcin H

## Homework Statement

10g of water at 0˚C added to 100g water at 50˚C

Qhot+Qcold=0
Q=mcΔT
Q=mL
Σmc(Tf-Ti)=0

## The Attempt at a Solution

So I understand this problem, but I'm not sure when I am supposed to use Q=mL, L being the latency, I think. So with the problem mentioned you can do:

mw*cw(Tf-0) + mw*cw(Tf-50) = 0 and solve for Tf. Tf= 45.45˚K

What if I had a problem like
10g ice at 0˚C added to 100g water at 50˚C? Do you write the equation step by step starting at ice? And do I use Q=mL to account for phase changes only? [solid to liquid] and [liquid to gas]?

mice*cice(Tf-0) + mL +mw*cw(Tf-50) = 0

Solve for TF. I think this is set up correctly, but I am not sure. Can you explain the mL part more? Is that the mass of ice * the latency of ice? This is where I get confused on how to do these problems.

Marcin H said:
mw*cw(Tf-0) + mw*cw(Tf-50) = 0 and solve for Tf. Tf= 45.45˚K
Careful with the units there.

Marcin H said:
What if I had a problem like
10g ice at 0˚C added to 100g water at 50˚C? Do you write the equation step by step starting at ice? And do I use Q=mL to account for phase changes only? [solid to liquid] and [liquid to gas]?
Yes.

Marcin H said:
mice*cice(Tf-0) + mL +mw*cw(Tf-50) = 0

Solve for TF. I think this is set up correctly, but I am not sure. Can you explain the mL part more? Is that the mass of ice * the latency of ice?.
Yes. Starting from ice, you have to convert the water from a solid to a liquid first, and that will require heat.

DrClaude said:
Yes. Starting from ice, you have to convert the water from a solid to a liquid first, and that will require heat.

Would you have to do this any time there is a phase change?? No matter what direction, ie liquid to solid or solid to liquid and all the rest. Will the latent heat be given for each phase if there is one?

Marcin H said:
Would you have to do this any time there is a phase change?? No matter what direction, ie liquid to solid or solid to liquid and all the rest. Will the latent heat be given for each phase if there is one?
View attachment 95499
With a substance like water, the values of the latent heat can be looked up.

Remember, the latent heat of fusion ≠ latent heat of vaporization.

SteamKing said:
With a substance like water, the values of the latent heat can be looked up.

Remember, the latent heat of fusion ≠ latent heat of vaporization.
Ok, thanks!

Yes, you have to take into account latent heat for any phase transition. Pay also attention to the sign of the change: for example, when going from solid to liquid, heat enters the substance without any change in temperature, while going from liquid to solid, heat is released from the substance without any change in temperature.

Marcin H

## 1. What is the difference between heat and internal energy?

Heat is the transfer of energy between two objects or systems due to a temperature difference. Internal energy, on the other hand, is the total energy contained within a system, including both kinetic and potential energy.

## 2. How does temperature affect heat transfer?

The rate of heat transfer is directly proportional to the temperature difference between two objects or systems. This means that the greater the temperature difference, the faster heat will be transferred.

## 3. What is the First Law of Thermodynamics?

The First Law of Thermodynamics states that energy cannot be created or destroyed, only transferred or converted from one form to another. This means that the total energy within a closed system remains constant.

## 4. How does heat flow in a closed system?

Heat always flows from a higher temperature to a lower temperature until thermal equilibrium is reached. This means that the temperature of the two objects or systems will eventually become equal.

## 5. How is internal energy related to work and heat?

According to the First Law of Thermodynamics, the change in internal energy of a system is equal to the sum of the work done on the system and the heat transferred to the system. This means that any change in internal energy can be explained by changes in work and/or heat.

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