Zeroth law of thermodynamics and thermometers

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SUMMARY

The Zeroth Law of Thermodynamics establishes that if two systems, A and C, are each in thermodynamic equilibrium with a third system, B, then A and C are also in thermodynamic equilibrium. This principle is crucial for understanding how thermometers function; when a thermometer measures the temperature of hot water, it reaches equilibrium with that water. However, when measuring cold water afterward, the thermometer must reach a new equilibrium, indicating that the two water samples are not in thermal equilibrium with each other despite the thermometer being in equilibrium with both at different times.

PREREQUISITES
  • Understanding of thermodynamic equilibrium
  • Basic knowledge of temperature measurement
  • Familiarity with the concept of systems in thermodynamics
  • Knowledge of the Zeroth Law of Thermodynamics
NEXT STEPS
  • Study the implications of the Zeroth Law of Thermodynamics in practical applications
  • Learn about different types of thermometers and their operating principles
  • Explore the concept of thermal equilibrium in multi-system scenarios
  • Investigate the First and Second Laws of Thermodynamics for a comprehensive understanding
USEFUL FOR

Students of physics, educators teaching thermodynamics, and professionals in fields requiring precise temperature measurements will benefit from this discussion.

demonelite123
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the 0th law of thermodynamics states that if 2 systems A and C are in thermodynamic equilibrium with a 3rd system B, then A and C are in thermodynamic equilibrium.

in other words, if A has the same temperature as B and B has the same temperature as C, then A has the same temperature as C.

I am a little confused with thermometers however. Let's say you use a thermometer to measure some very hot water. The thermometer and the very hot water are the 2 systems and when they come to thermodynamic equilibrium we get a reading. Then let's use the thermometer to measure some very cold water and we get a reading as well. The readings are obviously different. But if the thermometer is in thermodynamic equilibrium with the hot water and cold water then by the 0th law shouldn't the hot and cold water be in thermodynamic equilibrium with each other? but that must mean they have the same temperature which makes no sense at all. this has been confusing me greatly. can someone help explain this? thanks.
 
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Systems A and C must be in thermal equilibrium with B at the same time.
 
now that makes sense. thanks for your reply!
 

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