How Does Melting Ice Affect Entropy in a Calorimeter System?

In summary, the problem involves finding the net change in entropy of a system when 1.0 g of water at 20 degrees Celsius is mixed with 1.0 g of ice at 0 degrees Celsius in a well-insulated calorimeter. The heat of fusion of ice is needed to completely melt the ice, and since the temperature remains constant throughout the process, the change in entropy can be calculated by dividing the total heat required by the temperature in Kelvin. The units for entropy are typically joules per kelvin (J/K).
  • #1
laxplayer1189
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Homework Statement


What is the net change in entropy of the system from the time of mixing until the moment the ice completely melts? The heat of fusion of ice is .
Note that since the amount of ice is relatively small, the temperature of the water remains nearly constant throughout the process. Note also that the ice starts out at the melting point, and you are asked about the change in entropy by the time it just melts. In other words, you can assume that the temperature of the "ice water" remains constant as well.


In a well-insulated calorimeter, 1.0 of water at 20 is mixed with 1.0 of ice at 0.

Homework Equations





The Attempt at a Solution

 
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  • #2
Entropy is defined as dS = dQ/T (dS = change in entropy, dQ = change in heat, T = temperature in kelvin). Since the temperature is constant, all you have to do is take the total heat required to melt the ice and divide by the temperature in kelvin (i think, anyways!). Oh, and i was just wandering where the units are?
 
  • #3


The net change in entropy in this system can be calculated by considering the entropy of each component at different stages of the process. Initially, the entropy of the water and ice are both at their respective ambient temperatures, which means they have a relatively low entropy. As the ice melts, the entropy of the system increases due to the increase in disorder and randomness as the solid ice turns into liquid water. This increase in entropy is accompanied by a decrease in the temperature of the ice water mixture, as the ice absorbs heat from the water to melt.

Once all the ice has melted, the temperature of the water will reach equilibrium with the ice water mixture and the entropy of the system will remain constant. This means that the net change in entropy is equal to the increase in entropy during the melting process.

To calculate this change in entropy, we can use the equation ΔS = Q/T, where ΔS is the change in entropy, Q is the heat added to the system, and T is the temperature at which the heat is added. In this case, the heat added is the heat of fusion of ice, which is provided in the problem statement. Since the temperature of the ice water mixture remains constant throughout the process, we can use the initial temperature of 0 degrees Celsius to calculate the change in entropy.

Therefore, the net change in entropy is equal to the heat of fusion of ice divided by the initial temperature of the ice water mixture, or ΔS = (334 J/g) / (273 K) = 1.22 J/K. This means that the net change in entropy in this system is 1.22 J/K.
 

What is "Net change in entropy"?

"Net change in entropy" refers to the overall change in the amount of disorder or randomness in a system. It is a measure of the amount of energy that is available to do work in a system.

How is "Net change in entropy" calculated?

The net change in entropy is calculated by subtracting the initial entropy of a system from its final entropy. This can be calculated using the formula: ΔS = Sfinal - Sinitial.

Why is "Net change in entropy" important in science?

The concept of net change in entropy is important in science because it helps us understand and predict the direction of chemical reactions, physical processes, and other natural phenomena. It also plays a crucial role in the second law of thermodynamics, which states that the total entropy of a closed system will always increase over time.

What factors can cause a "Net change in entropy"?

The net change in entropy can be caused by a variety of factors, including changes in temperature, pressure, volume, or the addition or removal of energy. Chemical reactions, physical processes, and natural phenomena can also result in a net change in entropy.

How can "Net change in entropy" be affected by human activities?

Human activities can affect the net change in entropy in various ways. For example, burning fossil fuels and other industrial processes can increase the net entropy in the environment, leading to negative impacts on the planet's ecosystems. On the other hand, sustainable practices and efficient use of energy can help reduce the net change in entropy and promote a healthier environment.

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