# What is the final temperature of the mixture?

• FlyDoc
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## Homework Statement

10 g of water from a water ice mixture (0 degrees C) is added to100 g of water at 20 degrees celsius. what is the final temperature of the mixture? C of water =1 kcal/kg*C Latent Heat of Fusion of water=79.7 kcal/kg

Q=mC(Tf-Ti)
Q=mL

## The Attempt at a Solution

I ignored Latent heat of fusion since the 0 degree water form the water-ice is already melted. I just set mC(Tf-Ti) of water from water-ice equal to mC(Tf-Ti) of water. I got 22 degrees. Book answer is 18.2. Where am I going wrong?

Last edited by a moderator:

Probably a sign error: One part heats up, one part cools down, so you have to swap the sign on one side. Otherwise, you add the same amount of heat to both parts.

If you mix water at 0C with some other water at 20C, then the final temp of the mixture must be between 0C and 20C.

FlyDoc said:

## The Attempt at a Solution

I ignored Latent heat of fusion since the 0 degree water form the water-ice is already melted. I just set mC(Tf-Ti) of water from water-ice equal to mC(Tf-Ti) of water. I got 22 degrees. Book answer is 18.2. Where am I going wrong?

mC(Tf-Ti) for water and for ice are of equal magnitude but of opposite signs, as the warm water loses heat while the cold water gains.
The sum of the mC(Tf-Ti) terms is zero.

ehild

when 260g of metal shots at 200^C are mixed in an ice-water bath (m of ice is 50g, m of water is 90g) which is in a 105 g copper container, the final temperature of the mixture was 10^C. assuming no heat energy was lost from the system, what is the value of the specific heat capacity of the metal

## 1. What factors affect the final temperature of a mixture?

The final temperature of a mixture is affected by several factors, including the initial temperatures of the substances being mixed, the specific heat capacities of the substances, and the amounts of each substance in the mixture.

## 2. How can the final temperature of a mixture be calculated?

The final temperature of a mixture can be calculated using the formula Q = m * c * ΔT, where Q is the heat transferred, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.

## 3. Can the final temperature of a mixture be lower than the initial temperatures of the substances?

Yes, the final temperature of a mixture can be lower than the initial temperatures of the substances. This can occur if the substances have different specific heat capacities or if one substance has a higher mass than the other.

## 4. How does the mixing process affect the final temperature of a mixture?

The mixing process affects the final temperature of a mixture by allowing the heat to distribute evenly between the substances. This can result in the final temperature being closer to the average of the initial temperatures of the substances.

## 5. How does the type of container used for mixing affect the final temperature of a mixture?

The type of container used for mixing can affect the final temperature of a mixture by either insulating or conducting heat. For example, a metal container will conduct heat better than a plastic container, resulting in a higher final temperature.

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