Final Temp of Water Mixture: 28.46°C

In summary, the final temperature of the mixture of 25g of water at 10 degrees Celsius and 40g of water at 80 degrees Celsius is approximately 53 degrees Celsius. This can be calculated by setting the heat lost by the colder water equal to the heat gained by the hotter water, using the equation Qlost + Qgained = 0, and solving for the final temperature (Tf). Remembering that delta T = Tf - Ti, the final temperature can be found to be 53 degrees Celsius.
  • #1
Durin
11
0

Homework Statement


If 25g of water at a temperature of 10 degrees Celsius is mixed with 40 grams of water at 80 degrees Celsius what is the final temperature of the mixture?

Homework Equations


Qlost + Qgained = 0
Q=mcΔt

The Attempt at a Solution


Attempt 2:
0.025(4186)(x-10) + (0.04)(4186)(x-40) = 0
x = 28.46

I don't know if I'm doing this right...
 
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  • #2
Durin said:
I don't know if I'm doing this right...

You have the right idea, just remember that delta T = Tf - Ti

So the water at 10 degrees is going to heat to some final temperature T, and the water at 80 degrees is going to cool to the same temperature T

we don't need the specific heat of water since it's common in both terms

(0.025)(10 - x) = (0.04)(x-80)

x = 53 degrees

Also note in your equation - your heat is 40 degrees rather than what the question states - 80 degrees. Perhaps you were thinking of 40g

hope this helps,

cheers
 
  • #3
Thank you so much!
 

Related to Final Temp of Water Mixture: 28.46°C

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

The final temperature of a water mixture is affected by various factors such as the initial temperature of the water, the mass of each component, and the heat capacity of the materials involved. Other factors that may influence the final temperature include the rate of mixing, the ambient temperature, and the presence of impurities.

2. How is the final temperature of a water mixture calculated?

The final temperature of a water mixture can be calculated using the principle of heat transfer, which states that the total heat lost by the hot component is equal to the total heat gained by the cold component. By equating the heat lost and gained, the final temperature can be determined using the specific heat capacity and masses of the materials involved.

3. Can the final temperature of a water mixture be lower than the initial temperatures of both components?

Yes, it is possible for the final temperature of a water mixture to be lower than the initial temperatures of both components. This can occur if the hot component has a higher heat capacity and mass compared to the cold component, resulting in a greater heat transfer and a decrease in the final temperature. Additionally, if the cold component has impurities that lower its heat capacity, it can also contribute to a decrease in the final temperature.

4. How does the final temperature of a water mixture change when the mass of one component is increased?

The final temperature of a water mixture will generally increase when the mass of one component is increased. This is because a larger mass of a component will result in a greater amount of heat transfer, leading to a higher final temperature. However, this may also depend on the heat capacity of the materials involved and the initial temperatures of the components.

5. Can the final temperature of a water mixture be accurately predicted?

The final temperature of a water mixture can be accurately predicted using the principles of thermodynamics and heat transfer. However, this may require precise measurements and knowledge of the specific heat capacities and masses of the materials involved. Factors such as heat loss to the surroundings and impurities in the components may also affect the accuracy of the prediction.

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