# Latent Heat and final temperature

• Meowzers
In summary, the problem involves injecting steam at 100°C into 1.8 kg of water at 22°C in a well-insulated container. After the steam condenses and mixes with the water, the final temperature is 25°C. The goal is to find the mass of the injected steam. Using the equations for specific heat and latent heat of vaporization, the correct approach is to calculate the heat released by the steam at 100°C and add it to the heat needed to raise the water from 22°C to 25°C. Setting this equal to the heat required by the water, the mass of the injected steam is found to be 0.00877 kg.
Meowzers

## Homework Statement

Steam at 100°C is injected into 1.8 kg of water at 22°C in a well-insulated container, where it condenses and mixes with the existing water, reaching thermal equilibrium. If the final temperature of the well-mixed water is 25°C, what is the mass of the injected steam?

## Homework Equations

Q=(latent heat of vaporization)*m
Specific heat: Q=cmT

## The Attempt at a Solution

Latent heat of vaporization of water: 2.26*10^6 (J/kg)

Well, I thought that Q is the amount of heat that is being released as the steam is condensed into water.
Steam: Q=2.26*10^6 * m (m is what I'm trying to find)

The amount of heat being released from the steam condensing to water is the amount of heat that raises the temperature of the water from 22C to 25C.
Water: Q=cmT
Q=(4178 J/kg*K)*(1.8 kg)*(25-22)
Q=22561.2 J

Then, I set the Q's equal to each other to get 0.009, which is incorrect.

Do I need to account for the change of the steam's temperature frorm 100C to 25C? Or add in the unknown mass (I got roughly the same answer 0.010038 kg)?

You do have to consider the temperature change of the condensed steam from 100C to 25C. I don't think you did your revised calculation correctly.

So, I use the specific heat equation to calculate the heat released by the steam?

Q=cmT (steam)
Q=(4178 J/kg*K)*(m)*(100-25)
Q=13350*m

Then, I just added the 2 Q's together and set it equal to the specific heat stuff of the water.

(2.26*10^6)(m) + 313350m = (4178)(1.8)(3)
2573350m = 22561.2
m = 0.00877 kg

Is this the correct approach? Or should I have not added the Q's together?

Nevermind, I got it. Thanks for the response!

## 1. What is latent heat?

Latent heat is the amount of energy required to change the state of a substance without changing its temperature. This means that the substance absorbs or releases energy during a phase change, such as melting or vaporization, but its temperature remains constant.

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

In order for a substance to reach its final temperature, it must first undergo a phase change. This requires the absorption or release of latent heat. Once the phase change is complete, the substance can then continue to change temperature until it reaches its final temperature.

## 3. What factors affect the amount of latent heat required for a substance to change state?

The amount of latent heat required for a substance to change state depends on its specific heat capacity, the initial and final temperatures, and the type of phase change (e.g. from solid to liquid or liquid to gas).

## 4. How is latent heat calculated?

The amount of latent heat required for a substance to change state can be calculated using the formula Q = mL, where Q is the energy absorbed or released, m is the mass of the substance, and L is the latent heat of the substance.

## 5. Can the final temperature of a substance be predicted using latent heat?

No, the final temperature of a substance cannot be predicted solely based on its latent heat. Other factors, such as the initial temperature and the specific heat capacity, also play a role in determining the final temperature.

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