Calculating Final Temp of a mixture

In summary, the problem is to calculate the final temperature of a mixture of ice and water with given quantities and heat capacities, assuming no heat loss. The enthalpy of fusion for ice is also provided. The recommended equations for solving this problem are listed in the given links.
  • #1
viper2308
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0

Homework Statement


A 22.0 g sample of ice at -12.0°C is mixed with 120.0 g of water at 86.0°C. Calculate the final temperature of the mixture assuming no heat loss to the surroundings. The heat capacities of H2O(s) and H2O(l) are 2.08 and 4.18 J/g°C, respectively, and the enthalpy of fusion for ice is 6.02 kJ/mol


Homework Equations


I am not at home and don't have my book and the homework is due at 6:30 tonight so I can't figure out how to do this.


The Attempt at a Solution


I have no idea what equations to use to even try an attempt. Please Help.
 
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  • #3


I would first identify the key information and variables in the problem. The key information includes the mass and initial temperatures of the ice and water, as well as the heat capacities and enthalpy of fusion for water. The variables are the final temperature of the mixture and the amount of heat transferred between the ice and water.

Next, I would use the principles of thermodynamics to solve the problem. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or converted from one form to another. In this case, the heat lost by the water as it cools down will be gained by the ice as it warms up.

To calculate the final temperature of the mixture, we can use the equation:

m1c1(Tf - Ti) + m2c2(Tf - Ti) = 0

Where m1 and m2 are the masses of the ice and water respectively, c1 and c2 are the heat capacities of ice and water, Ti is the initial temperature of the ice and water, and Tf is the final temperature of the mixture.

Substituting the given values, we get:

(22 g)(2.08 J/g°C)(Tf - (-12.0°C)) + (120 g)(4.18 J/g°C)(Tf - 86.0°C) = 0

Solving for Tf, we get:

Tf = [-(22 g)(2.08 J/g°C)(-12.0°C) + (120 g)(4.18 J/g°C)(86.0°C)] / [(22 g)(2.08 J/g°C) + (120 g)(4.18 J/g°C)]

Tf = 12.77°C

Therefore, the final temperature of the mixture is 12.77°C. It is important to note that this calculation assumes no heat loss to the surroundings, which may not be realistic in a real-world scenario.
 

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

To calculate the final temperature of a mixture, you will need to know the initial temperatures and quantities of each substance in the mixture, as well as their specific heat capacities. Then, you can use the formula 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. By equating the heat transferred from one substance to the heat transferred to the other substance, you can solve for the final temperature.

2. What is the specific heat capacity of a substance?

The specific heat capacity of a substance is the amount of heat energy required to raise the temperature of 1 gram of the substance by 1 degree Celsius (or 1 Kelvin). It is often denoted by the symbol C and has units of J/g°C or J/gK.

3. Can you calculate the final temperature of a mixture without knowing the specific heat capacities?

No, it is not possible to calculate the final temperature of a mixture without knowing the specific heat capacities of the substances involved. The specific heat capacity is a crucial factor in determining how much heat energy is required to change the temperature of a substance, and without this information, the final temperature cannot be accurately calculated.

4. What other factors can affect the final temperature of a mixture?

Apart from the initial temperatures and specific heat capacities, the final temperature of a mixture can also be affected by external factors such as pressure, changes in state (i.e. solid to liquid or liquid to gas), and the presence of impurities. These factors can alter the heat transfer and change the final temperature.

5. Can the final temperature of a mixture ever be lower than the initial temperatures?

Yes, the final temperature of a mixture can be lower than the initial temperatures if one of the substances in the mixture has a negative heat capacity (meaning it releases heat when its temperature increases). In this case, the heat released by one substance can offset the heat gained by the other substance, resulting in a lower final temperature.

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