What is the change in entropy when mixing water and alcohol?

In summary, the problem involves mixing 0.5 kg of water at 5.6 oC with 1.3 kg of alcohol at 65.9 oC, and finding the change in entropy of the system. Using specific heat capacities of 4186 J/(kgoC) for water and 2430 J/kgoC for alcohol, the final temperature is calculated to be 41.87 oC. The change in entropy is then found to be 2778 J/C, which is incorrect. By converting temperatures to Kelvin and mass to grams, using specific heat capacities of 4.186 J/g-K for water and 2.4 J/g-K for alcohol, the final temperature is calculated to be
  • #1
huybinhs
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0

Homework Statement



0.5 kg of water at a temperature of 5.6 oC is mixed with 1.3 kg of alcohol at 65.9 oC. They come to equilibrium. What is the change in entropy (in J/K) of the system when the two liquids are mixed?

Hint:
The specific heat capacity for water is 1 kcal/kgoC = 4186 J/(kgoC), and for alcohol it is 0.58 kcal/kgoC = 2430 J/kgoC.

2. The attempt at a solution

I calculate Tf = [m1c1T1+m2c2T2] / [(m1c1) + (m2c2)] = 41.87*C

then Delta S = m1c1 ln(Tf/T1) + m2c2 ln (Tf/T2) = 2778 J/C

Then I convert to J/K which is divide it by 274.15 = 10.13 J/K = INCORRECT!

This is a messy problem. Please help!
 
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  • #2
Try Cp(water)=4.186 J/g-k and Cp(alcohol)=2.4 J/g-K. Convert temperatures to K and mass to grams. I assume your equations are accurate and the problem is related to units.
 
  • #3
RTW69 said:
Try Cp(water)=4.186 J/g-k and Cp(alcohol)=2.4 J/g-K. Convert temperatures to K and mass to grams. I assume your equations are accurate and the problem is related to units.

Should I take 1 C = 274.15 K or 273 K?
 

What is entropy?

Entropy is a measure of the disorder or randomness in a system. It is a thermodynamic quantity that describes the amount of energy that is unavailable for work in a system.

What causes a change in entropy?

A change in entropy can be caused by a number of factors, including changes in temperature, pressure, or volume of a system. It can also be influenced by chemical reactions, mixing of substances, and the transfer of energy.

How is entropy related to the second law of thermodynamics?

The second law of thermodynamics states that the total entropy of an isolated system will always increase over time. This means that in any natural process, the total amount of disorder or randomness in the system will never decrease.

How do you calculate the change in entropy?

The change in entropy of a system can be calculated using the equation ΔS = Qrev/T, where ΔS is the change in entropy, Qrev is the reversible heat transfer, and T is the temperature in Kelvin. This equation is known as the Clausius inequality and is a fundamental concept in thermodynamics.

What are some real-world applications of the change in entropy problem?

The concept of entropy and its change is important in many areas of science and engineering. It is used to understand and predict the behavior of chemical reactions, the efficiency of engines and power plants, and the stability of materials and systems. It also has applications in fields like biology, economics, and information theory.

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