# Temp equilibrium / latent heat

In summary, a 625g iron block at 352 C is placed in a container with 40g of water at 15 C. The equilibrium temperature of the system is 243 C, but since water boils at 100 C, some of the water vaporizes. To find out how much water vaporizes, we can compare the heat lost by the iron block to the heat gained by the water, taking into account the latent heat of evaporation.

## Homework Statement

1 625g iron block is heared to 352 C is placed in an insulate container (of negligible heat capacity) containing 40g of water at 15 C. what is the equilibrium temp of this system? if your answer is 100 C, determine the amount of water that has vaporized.

## Homework Equations

Q(block)=mc(T-Tblock) = .625(560)(T-352)
Q(water)=.040(4186)(T-15)

## The Attempt at a Solution

set Q(block)=Q(water) i got T=242.95.. how was i suppose to get 100 C?

how do i solve how many grams of water have evaporated.

im so lost on this probelm, any help would be appreciated.

When water reaches 100 C it turns to steam (it boils). To turn 1g of water at 100 C into 1g of steam at 100 C requires heat energy. That energy is called the "latent heat of evaporation".

You are doing OK so far. The equilibrium temp would have been 243 if the water didn't boil. but we know water boils at 100, therefore some water DID boil.

Heat out of block as it cools to 100 = heat into water to raise all the water to 100 + latent heat to convert some of the water to steam at 100.

To solve this problem, you need to consider the concept of thermal equilibrium and latent heat. When two objects of different temperatures are placed in contact, they will exchange heat until they reach the same temperature. In this case, the iron block is initially at 352 C and the water is at 15 C. The heat from the iron block will transfer to the water until they both reach the same temperature.

To find the equilibrium temperature, you can use the equation Q(block) = Q(water), where Q represents the heat transferred. You correctly set up the equations for the heat transferred by the iron block and the water, but you forgot to include the heat of vaporization for the water. This is the amount of energy required to change the water from liquid to gas.

The correct equation should be:

Q(block) = Q(water) + Q(vaporization)

Where Q(vaporization) = m(water) * L, where L is the latent heat of vaporization for water (2260 kJ/kg).

Substituting the values in the equation, you will get:

.625(560)(T-352) = .040(4186)(T-15) + .040(2260)

Solving for T, you will get T = 100 C, which is the equilibrium temperature for the system.

To determine the amount of water that has vaporized, you can use the equation for Q(vaporization) and solve for m(water):

Q(vaporization) = m(water) * L

Substituting the values, you will get:

.040(2260) = m(water) * (2260)

Solving for m(water), you will get m(water) = 0.040 kg, which is the amount of water that has vaporized.

I hope this helps clarify the problem for you. Remember to always consider all the relevant factors, such as latent heat, when solving thermodynamics problems.

## 1. What is the definition of temperature equilibrium?

Temperature equilibrium is a state in which two or more objects or substances have the same temperature and there is no net transfer of heat between them. This means that the rate of heat transfer from one object to another is equal to the rate of heat transfer in the opposite direction.

## 2. How is temperature equilibrium related to latent heat?

Latent heat is the amount of heat required to change the state of a substance without changing its temperature. When a substance is at its melting or boiling point, adding or removing heat will not cause a change in temperature until the phase change is complete. Therefore, temperature equilibrium is reached during the phase change process when the substance's temperature remains constant despite the transfer of heat.

## 3. What is the difference between latent heat of fusion and latent heat of vaporization?

The latent heat of fusion is the amount of heat required to change a substance from a solid to a liquid at its melting point, while the latent heat of vaporization is the amount of heat required to change a substance from a liquid to a gas at its boiling point. Both are types of latent heat and are related to temperature equilibrium during phase changes.

## 4. How does the latent heat of a substance affect its temperature?

During a phase change, the latent heat of a substance absorbs or releases energy without causing a change in temperature. This is because the energy is being used to break or form intermolecular bonds between the particles of the substance. This means that the temperature of a substance will remain constant until the phase change is complete.

## 5. Can temperature equilibrium be achieved without latent heat?

No, temperature equilibrium during phase changes is dependent on the presence of latent heat. If there is no latent heat, the temperature of a substance will continue to increase or decrease as heat is added or removed, even during a phase change. Temperature equilibrium can only be reached when there is a transfer of latent heat during a phase change process.

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