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# ZEROTH LAW OF THERMODYNAMICS

• Based on the other three laws, zeroth thermodynamics law is formulated. Still, at the time of discovery, lots of confusion occurred about the naming, whether to name it as fourth law or something else.
• This confusion got sorted as a clear definition of temperature and its occurrence. Hence, it is named Zeroth law of thermodynamics.
• The zeroth law indicates the temperature changes and heat flows from one system to another in thermal equilibrium.

## STATE ZEROTH LAW OF THERMODYNAMICS

• When a body ‘P’ is in thermal equilibrium with another body ‘Q’, and also separately in thermal equilibrium with a body ‘R’, then body ‘Q’ and ‘R’ will also be in thermal equilibrium with each other.
• The above statement defines the zeroth law of thermodynamics, which is based on thermal equilibrium.
• If two systems present in the thermal equilibrium exist at the same temperature, the Zeroth law of thermodynamics is applicable. One can express zeroth law in many ways, but this is one of the simplest ways.
• This law found that temperature is the measure of something, as it flows from a hot body to a cold body by the mode of radiation in heat transfer. This gave the mathematical definition of temperature.
• Zeroth law also states that there is no heat flow if the system is present in the thermal equilibrium state.

### ZEROTH LAW OF THERMODYNAMICS EXAMPLES

• The system may be in thermal equilibrium if there is no heat transfer from one body to another even when they keep close to each other when the system attains the same temperature.
• For example, a cup of soup kept in a refrigerator overnight is said to be in thermal equilibrium with the air in the refrigerator. As heat no longer flows from the cup of soup( one source) to the refrigerator (the other source) or back
• The flow of heat between the two systems can be measurable, and regardless of the distance, the heat flow between the two systems.

Let P, Q, and R be three systems. If P and R are in thermal equilibrium, and P and Q are in thermal equilibrium, then Q and R are in thermal equilibrium.

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The above statement is given in symbolic representation here. All the systems in the thermal equilibrium are at the same temperature.

Here are some of the examples of the zeroth law of thermodynamics listed below.

• After some time, the cup of tea will become cold
• hot water and cold water
• Thermometer
• The thermostat in your room
• When a heated and a cold body are brought close together, the hot body loses heat and the cold body starts to heat up. But the transfer of heat flows from hotter to the colder body. The flow of heat stops when both the systems attain thermal equilibrium.
• The law of conservation of energy in the colder system is defined as: the amount of heat loss by the hotter body is equal to the amount of heat gained by the colder body.
• Thermal equilibrium is attained by placing the cup of hot tea in the surrounding area. After some time the cup of tea becomes cold as the heat flows from the cup to the atmosphere until both the surrounding temperature and the tea’s temperature become the same.
• If the cup of tea is 80°C and the surrounding temperature is 30°C , the tea will lose its heat until its temperature reaches 30 degrees. Here a hot cup of tea acts like the zeroth law of thermodynamics.

• Let us say the thermostat in your room is 25 degrees, wherein your room temperature and the thermostat temperature is the same(thermal equilibrium).
• According to the zeroth law of thermodynamics, all the furniture, bed, sofa, tables will have the same 25 degrees of temperature.

#### HOT WATER AND COLD WATER

• As we saw in the above example, we place one cup of ice and another cup of hot water.
• Let us assume that the atmospheric temperature is 25 degrees celsius, ice is at 0°C, and hot water is at 80 degrees.
• The ice at 0°C melts and turns into water of temperature 25 degrees Celsius, the same as the atmospheric temperature.
• Same in the case of hot water, the heat flows from hot water to the surrounding until both the hot water and the surrounding temperature are the same (25 Degree Celsius)

• Like everyone, if we keep the fruits in the refrigerator, the temperature of the fruits decreases and takes the temperature of the refrigerator air.

#### THERMOMETER FOR MEASURING  THE BODY TEMPERATURE

• When your body temperature increases due to fever, the mercury level in the thermometer increases and attains the same temperature as that of the body (thermal equilibrium)
• The temperature of mercury drops after losing contact with the body. It is due to the expansion of the mercury inside the glass tube.

## THERMAL EQUILIBRIUM

• We use the term equilibrium when the temperature of the two systems is equal.
• In thermal equilibrium, the net force is zero.
• The pressure, temperature and volume remains constant throughout the thermodynamic equilibrium.
• If the temperature within the system is uniformed and temporarily constant, the system is said to be thermally in equilibrium.
• Systems in thermodynamic equilibriums are always in thermal equilibrium, but the systems in thermal equilibrium are not always in thermodynamic equilibrium.
• In thermal equilibrium, there may be the transfer of energy in the form of internal energy, but matter and energy in this form can’t be transferred.

### THERMAL EQUILIBRIUM DEFINITION

• Thermal equilibrium is the part of thermodynamics. The thermodynamic equilibrium is of two types is of three types :
1. Mechanical equilibrium
2. Chemical equilibrium
3. Thermal equilibrium
• Thermal equilibrium is when there is no net flow of thermal energy from one system to another and has the same temperature; it also obeys the zeroth law of thermodynamics.
• Both thermal and thermodynamic equilibrium are different from each other , so don’t confuse them.

### IMPORTANCE OF ZEROTH LAW OF THERMODYNAMICS

• Consider two systems, P and Q, separated by an adiabatic wall that does not allow any exchange of energy between them. The third system, R, is separated from systems P and Q by a conducting or diathermic wall, as shown in the figure.
• Since an adiabatic wall is present between P and R, they attain thermal equilibrium, and similarly, R and Q are in thermal equilibrium.
• In other words, both systems P and Q are in thermal equilibrium with the third system R, separately.
• When the adiabatic wall between systems P and Q is removed, no energy transfer occurs between them. It shows that systems P and Q are also in thermal equilibrium. From this observation, one can know the importance of Zeroth law.