Zeroth Law of Thermodynamics
The Zeroth Law of Thermodynamics is the most fundamental law of thermodynamics. It introduces the concept of temperature and provides the basis for measuring temperature. The law explains thermal equilibrium and forms the foundation of all temperature-measuring devices.
Introduction
In everyday life, we compare objects by saying that one object is hotter or colder than another. To make this comparison scientifically, we need a measurable quantity called temperature. The Zeroth Law of Thermodynamics provides the scientific basis for defining temperature.
Statement of Zeroth Law
If two thermodynamic systems are separately in thermal equilibrium with a third system, then they are in thermal equilibrium with each other.
In simple words, if System A has the same temperature as System C, and System B also has the same temperature as System C, then Systems A and B must have the same temperature.
Thermal Equilibrium
Thermal equilibrium is the state in which no net heat transfer occurs between two systems in thermal contact.
When two bodies have different temperatures, heat flows from the hotter body to the colder body. This transfer continues until both bodies attain the same temperature.
At thermal equilibrium:
- No net heat transfer occurs.
- The temperatures of both systems become equal.
- The macroscopic properties of the systems remain unchanged.
Types of Walls
Adiabatic Wall
- An insulating wall.
- Does not allow heat transfer between systems.
Diathermic (Conducting) Wall
- Allows heat transfer between systems.
- Heat flows until thermal equilibrium is achieved.
Experimental Verification of Zeroth Law
Step 1: Separate Contact with System C
Consider three thermodynamic systems A, B, and C.
Systems A and B are separated from each other by an adiabatic wall. However, both A and B are separately connected to System C through conducting walls.
Heat flows between A and C until thermal equilibrium is reached.
Therefore,
\[ T_A = T_C \]
Similarly, heat flows between B and C until thermal equilibrium is reached.
Therefore,
\[ T_B = T_C \]
Step 2: Bringing A and B into Contact
Now System C is isolated using an adiabatic wall.
The wall between A and B is replaced with a conducting wall.
When A and B are allowed to exchange heat, no heat transfer occurs.
- No heat flows between A and B.
- Their temperatures remain unchanged.
- Their macroscopic properties remain stable.
This proves that A and B were already in thermal equilibrium.
Mathematical Representation
Since
\[ T_A = T_C \]
and
\[ T_B = T_C \]
therefore,
\[ T_A = T_B \]
This equation represents the Zeroth Law of Thermodynamics.
Temperature as a Physical Quantity
The Zeroth Law introduces temperature as a measurable physical quantity.
Temperature determines the direction of heat flow:
- Heat flows from higher temperature to lower temperature.
- No heat flows when temperatures are equal.
Therefore, temperature is the criterion for determining thermal equilibrium.
Thermometers and Zeroth Law
A thermometer works on the principle of the Zeroth Law.
When a thermometer is placed in contact with a body, heat is exchanged until thermal equilibrium is established.
At equilibrium,
\[ T_{\text{thermometer}} = T_{\text{body}} \]
The thermometer reading then gives the temperature of the body.
Real-Life Example
Consider System C as a thermometer.
When the thermometer is placed in hot water (System A), it reaches thermal equilibrium and records a temperature of \(100^\circ C\).
The same thermometer is then placed in another liquid (System B), and it again records \(100^\circ C\).
Since both systems are in thermal equilibrium with the same thermometer,
\[ T_A = T_B = 100^\circ C \]
Thus, both liquids have the same temperature even without direct contact.
Importance of Zeroth Law
- Provides the basis for the concept of temperature.
- Defines thermal equilibrium.
- Forms the foundation of temperature measurement.
- Makes thermometer construction possible.
- Allows comparison of temperatures of different systems.
- Serves as the foundation of thermodynamics.
Why is it Called the Zeroth Law?
The First and Second Laws of Thermodynamics had already been established before this principle was formally recognized.
In 1931, physicist R. H. Fowler pointed out that this law is more fundamental because it defines temperature itself.
Instead of renumbering the existing laws, it was named the Zeroth Law of Thermodynamics.
Applications of Zeroth Law
- Measurement of temperature using thermometers.
- Calibration of temperature scales.
- Weather monitoring instruments.
- Medical thermometers.
- Industrial temperature control systems.
- Scientific laboratory measurements.
Key Points to Remember
- The Zeroth Law establishes the concept of temperature.
- Thermal equilibrium means no net heat transfer.
- Equal temperatures imply thermal equilibrium.
- Thermometers operate on the Zeroth Law.
- If \(T_A=T_C\) and \(T_B=T_C\), then \(T_A=T_B\).
- The law forms the foundation of thermodynamics.
Frequently Asked Questions (FAQ)
Q1. What is the Zeroth Law of Thermodynamics?
It states that if two systems are separately in thermal equilibrium with a third system, they are in thermal equilibrium with each other.
Q2. What is thermal equilibrium?
Thermal equilibrium is the state in which no net heat transfer occurs between systems in thermal contact.
Q3. Why is temperature important?
Temperature determines the direction of heat flow and indicates whether systems are in thermal equilibrium.
Q4. Which instrument is based on the Zeroth Law?
A thermometer is based on the Zeroth Law of Thermodynamics.
Q5. Why is the law called the Zeroth Law?
Because it was recognized after the First and Second Laws but was found to be more fundamental than both.
Quiz
1. The Zeroth Law provides the basis for:
- (A) Pressure
- (B) Volume
- (C) Temperature
- (D) Density
Answer: (C) Temperature
2. Thermal equilibrium means:
- (A) Maximum heat transfer
- (B) No net heat transfer
- (C) Infinite temperature
- (D) Constant pressure
Answer: (B) No net heat transfer
3. An adiabatic wall:
- (A) Allows heat transfer
- (B) Prevents heat transfer
- (C) Produces heat
- (D) Absorbs heat
Answer: (B) Prevents heat transfer
4. If \(T_A=T_C\) and \(T_B=T_C\), then:
- (A) \(T_A>T_B\)
- (B) \(T_A\)
- (C) \(T_A=T_B\)
- (D) Cannot be determined
Answer: (C) \(T_A=T_B\)
5. A thermometer works on:
- (A) First Law
- (B) Second Law
- (C) Zeroth Law
- (D) Third Law
Answer: (C) Zeroth Law
No comments:
Post a Comment