Final Temperature of Copper-Water System

In summary, the problem involves a 505g piece of copper tubing being heated and placed in a vessel with 59.8g of water at different temperatures. The final temperature of the system can be found by using the equation q = c x mass x change in temperature and accounting for the heat capacity of the vessel by combining it with the water. The final temperature can be solved for by treating the heat gained/lost separately for each mass and using the common final temperature in both equations.
  • #1
grapejellypie
13
0

Homework Statement


A 505g piece of copper tubing is heated to 99.9 degrees C and placed in an insulated vessel containing 59.8g of water at 24.8 degrees C. Assuming no loss of water and a heat capacity for the vessel of 10.0 J/K, what is the final temperature of the system? (c of coppuer is 0.387 J/(gk))


Homework Equations



q = c x mass x change in temperature
change in termperature = T[final] - T[initial]

The Attempt at a Solution


I have no idea how to go about solving this problem
 
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  • #2
Heat lost = heat gained.
 
  • #3
how do you account for the two separate systems combining into one?
(i.e. how would you deal with the two different masses?)
 
  • #4
Treat heat gained/lost separately. Use equation you have already posted for each mass separately. The only commong thing in both equations will be the final temperature, and that's what you will solve for.
 
  • #5
how do you incorporate the heat capacity of the vessel?
 
  • #6
Combine it with water (simply add them, nothing more fancy). It coul be given as vessel mass and specific heat, but the heat capacity is the same, just details are hidden - which completely doesn't matter.
 

FAQ: Final Temperature of Copper-Water System

What is the formula for calculating final temperature?

The formula for calculating final temperature is Tf = (m1C1T1 + m2C2T2)/ (m1C1 + m2C2), where Tf is the final temperature, m is the mass of the substance, C is the specific heat capacity, and T is the initial temperature.

Can the final temperature be lower than the initial temperature?

Yes, the final temperature can be lower than the initial temperature if the substances involved have different specific heat capacities or if one substance loses heat to its surroundings.

How do I calculate final temperature when the substances are at different initial temperatures?

In this case, you can use the formula Tf = (m1C1T1 + m2C2T2)/ (m1C1 + m2C2), where T1 and T2 are the initial temperatures of the substances.

What units should be used when calculating final temperature?

The units for mass should be in grams (g) or kilograms (kg), the specific heat capacity in joules per gram Celsius (J/g°C) or joules per kilogram Celsius (J/kg°C), and the temperature in degrees Celsius (°C) or Kelvin (K).

Can I use this formula to calculate final temperature for any substances?

Yes, this formula can be used for any substances as long as the mass, specific heat capacity, and initial temperature are known. However, it is important to note that the specific heat capacity may vary depending on the substance, so it is best to use the specific heat capacity of the specific substance being studied.

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