Solving for Final Equilibrium Temperature of Water-Copper System

In summary, we have a system with 173 g of water at 20°C in a copper container of mass 327 g. An additional 129 g of water at 100°C is added. We can use the equation Q = mcΔT to find the final equilibrium temperature (in degrees C) if we treat the system's water and container as isolated. By setting the total heat gained equal to the total heat lost and solving for Tf, we get the correct answer for the final temperature.
  • #1
Sam Vermeulen
5
0

Homework Statement


173 g of water at 20°C is contained in a copper container of mass 327 g. An additional 129 g of water at 100°C is added. What is the final equilibrium temperature (in degrees C) if we treat the system's water and container as isolated?

Homework Equations


Q = mcΔT

The Attempt at a Solution



0 = mwater1c(Tf - Ti) + mwater2cwater(Tf - Ti) + mcopperccopper(Tf - Ti)
0 = (.173kg)(4.186kJ/kg°C)(Tf - 20°C) + (0.129kg)(4.186kJ/kg°C)(Tf - 100°C) + (.327kg)(.387kJ/kg°C)(Tf - 20°C)

I attempted to solve for Tf but the answer was not correct.
 
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  • #2
Hi Sam Vermeulen and welcome to PF.

The method is correct. Recheck your algebra.
 
  • #3
kuruman said:
Hi Sam Vermeulen and welcome to PF.

The method is correct. Recheck your algebra.
Thank you! I figured out where I was going wrong. Much appreciated.
 

What is the purpose of solving for the final equilibrium temperature of a water-copper system?

The purpose of this calculation is to determine the temperature at which a water-copper system will reach thermal equilibrium, or the point at which the two substances have the same temperature and no further heat transfer occurs between them. This is important in understanding and predicting the behavior of systems involving water and copper, such as in heat transfer processes or in the design of cooling systems.

What is the formula for solving for the final equilibrium temperature of a water-copper system?

The formula is given by Tf = (m1c1T1 + m2c2T2) / (m1c1 + m2c2), where Tf is the final equilibrium temperature, m1 and m2 are the masses of water and copper respectively, c1 and c2 are the specific heats of water and copper respectively, and T1 and T2 are the initial temperatures of water and copper respectively.

What are the assumptions made in solving for the final equilibrium temperature of a water-copper system?

The calculation assumes that the water and copper are in a closed system with no external heat sources, the system is well-insulated so there is no significant heat loss to the surroundings, the specific heats of water and copper remain constant throughout the process, and there is no phase change occurring in the water (i.e. it remains in liquid form).

Can this formula be applied to other systems besides water and copper?

Yes, this formula can be applied to any two substances in a closed system as long as the assumptions are met and the specific heats are known. However, it is important to note that the specific heats will vary for different substances, so the values used in the formula will be different.

How accurate is this calculation in predicting the final equilibrium temperature?

This calculation is fairly accurate as it takes into account the specific heats and masses of the substances involved. However, it is important to note that there may be slight variations due to external factors such as heat loss to the surroundings or changes in specific heat due to phase changes. Additionally, the accuracy may also depend on the accuracy of the specific heat values used in the formula.

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