# UCL WIKI

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• Zeroth law of thermodynamics
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# The zeroth law and temperature

"The temperature of a system is a property that determines whether or not a system is in thermal equilibrium with other systems".
The concept of thermal equilibrium is very familiar to us! For example, we all know that if we take a cold bottle of milk from the fridge and a cup of hot water and leave them in the room for a few hours, they both will have the same temperature as that of the room. That is they both reach thermal equilibrium with the room. Thus we say:
"Two systems are equal in temperature if no change in any property occurs when they are bought into communication".
We can also conclude that:
"Two systems which are equal in temperature to a third system are equal in temperature to each other".
This is the Zeroth Law of Thermodynamics and provides the basis for temperature measurements. Temperature and heat are discussed more in Energy interactions.

## Temperature Scales

Consider an experiment involving three systems S1, S­2 and S3. Suppose we bring S3 into contact with S1 until they reach thermal equilibrium. No work interactions assumed!
Now if we bring S3 into contact with S2 and as a result observable changes occur in S3¸ then we can conclude that the temperatures of S1 and S2 are unequal. To measure this inequality we use a thermometer.
For thermometer, we can use any property that changes with temperature. For example, if we chose a glass tube containing mercury as system S3, then we would have a mercury in glass thermometer. The mercury in glass thermometer is usually calibrated between two fixed points- one at the melting point of ice and the other at the boiling point of water- both at the pressure of one atmosphere.

Temperature scales are then defined by assigning numbers to the ice point and steam point and to the equally-spaced points between them.