Thermodynamic Entropy Clarification

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SUMMARY

The discussion focuses on calculating the change in entropy when mixing 0.6 kg of water at 25°C with 0.8 kg of alcohol at 30.5°C. The final equilibrium temperature is determined to be 300.55 K (27.4°C). The entropy change is calculated using the formula ∆S = Mw*Cw*ln(Tf/Tw) + Ma*Ca*ln(Tf/Ta). It is established that Kelvin must be used for entropy calculations to obtain accurate results, as using Celsius yields incorrect values.

PREREQUISITES
  • Understanding of thermodynamic principles, specifically entropy
  • Familiarity with specific heat capacities of substances
  • Knowledge of logarithmic functions in thermodynamic equations
  • Ability to perform unit conversions between Celsius and Kelvin
NEXT STEPS
  • Study the derivation and applications of the entropy formula in thermodynamics
  • Learn about specific heat capacities of various substances and their implications
  • Explore the concept of thermal equilibrium and its significance in thermodynamic processes
  • Investigate the role of temperature scales in scientific calculations, focusing on Kelvin vs. Celsius
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Students studying thermodynamics, educators teaching heat transfer concepts, and professionals involved in thermal system analysis.

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Homework Statement


We mix 0.6 kg of water at a temperature of 25°C with 0.8 kg of alcohol at 30.5°C. They
come to equilibrium. (Here's some useful data: The specific heat capacity for water is 1
kcal/kg°C = 4186 J/kg°C, and for alcohol it is 0.58 kcal/kg°C = 2430 J/kg°C

What is the change in entropy (in J/K) of the system when the two are mixed?

Homework Equations


∆S = ∆Sw + ∆Sa = Mw*Cw*ln(Tf /TW) + Ma*Ca*ln(Tf /Ta)


The Attempt at a Solution


I've calculated the final temperature to be 300.55 K or 27.4 C

so now the equation looks like:
.6*4186*Ln(Tf/Tw) + .6*2430*Ln(Tf/Ta) = dS

The problem is, do I use Kelvin or Celsius for the entropy calculation? I get two totally different values if I do either one... .0794 with K or 21.87 with C.
 
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You have to use Kelvin.
 

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