Solving Final Temperature of Copper-Water Mixture

In summary, the problem involves finding the final temperature of a mixture of copper and water after heat exchange. The specific heat capacities and initial temperatures of both substances are given, and the equation for heat exchange is used to find the final temperature. A slight rounding error may occur, but the correct solution is 23.7°C.
  • #1
sadifermi
5
0
I need help with a question. I think I have an answer, but don't know if it's right. It also doesn't add up to 0 if I plug in the final temperture into the equation. But I keep getting the same answer. Help please!

A 150 g piece of copper at 90°C is placed in 250 g of water at 20°C. Assume that no heat escapes into the surroundings. Find the final temperature of the mixture.

mass of copper: (0.150kg)
specific heat capacity: (390J/(kg°C))
temperture of copper: (t2-90°C)

mass of water: (0.250kg)
specific heat capacity: (4200J/(kg°C))
temperture of water: (t2-20°C))

equation: (mass of copper)(spec. heat cap.)(final temp - intial temp) + (mass of water)(spec. heat cap.)(final temp - initial temp) = 0

(0.150kg)(390J/(kg°C))(t2-90°C)+(0.250kg)(4200J/(kg°C))(t2-20°C))=0
1108.5t2=26265
t2 = 23.7°C
 
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  • #2
Heat Exchange of Copper and Water

Homework Statement



I need help with a question. I think I have an answer, but don't know if it's right. It also doesn't add up to 0 if I plug in the final temperture into the equation. But I keep getting the same answer. Help please!

A 150 g piece of copper at 90°C is placed in 250 g of water at 20°C. Assume that no heat escapes into the surroundings. Find the final temperature of the mixture.

mass of copper: (0.150kg)
specific heat capacity: (390J/(kg°C))
temperture of copper: (t2-90°C)

mass of water: (0.250kg)
specific heat capacity: (4200J/(kg°C))
temperture of water: (t2-20°C))

Homework Equations




equation: (mass of copper)(spec. heat cap.)(final temp - intial temp) + (mass of water)(spec. heat cap.)(final temp - initial temp) = 0

The Attempt at a Solution



(0.150kg)(390J/(kg°C))(t2-90°C)+(0.250kg)(4200J/(kg°C))(t2-20°C))=0
1108.5t2=26265
t2 = 23.7°C
 
  • #3


Correct solution!ehild
 
  • #4
sadifermi said:
t2 = 23.7°C
It's just rounding error. If you plug in 23.6942 you'll get something close to 0. But don't change your answer to that. 23.7 C is fine.
 
  • #5
Thanks! I appreciate it and the speedy reply!
 

1. How do you calculate the final temperature of a copper-water mixture?

The final temperature of a copper-water mixture can be calculated using the heat capacity and initial temperatures of both substances, as well as the mass and specific heat capacities of copper and water. This can be done using the equation Q = mCΔT, where Q is the heat transferred, m is the mass, C is the specific heat capacity, and ΔT is the change in temperature.

2. What is the specific heat capacity of copper and water?

The specific heat capacity of copper is 0.385 J/g°C, and the specific heat capacity of water is 4.184 J/g°C. These values are necessary for calculating the final temperature of a copper-water mixture.

3. Can the final temperature of a copper-water mixture be higher than the initial temperature of one of the substances?

Yes, it is possible for the final temperature of a copper-water mixture to be higher than the initial temperature of one of the substances. This can occur if the initial temperatures of both substances are significantly different and the amount of heat transferred is large enough.

4. How does the mass of each substance affect the final temperature of the mixture?

The mass of each substance plays a significant role in determining the final temperature of the mixture. The substance with the larger mass will have a greater influence on the final temperature, as it requires more heat to change its temperature compared to the substance with the smaller mass.

5. What is the importance of solving for the final temperature of a copper-water mixture?

Solving for the final temperature of a copper-water mixture is important in various scientific and practical applications. This information can be used to determine the efficiency of a heat transfer process, as well as to predict the behavior of other substances when mixed together. It is also useful in industrial settings where precise temperature control is necessary.

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