Notes : Thermal Equilibrium: Adiabatic & Diathermic Walls | Class 11 Physics
1. Defining Thermal Equilibrium
The concept of equilibrium has different meanings in mechanics and thermodynamics.
Mechanical Equilibrium
A system is said to be in mechanical equilibrium when the net external force and the net torque acting on it are zero.
This condition is related to motion, forces, and balance.
Thermodynamic Equilibrium
A system is said to be in thermodynamic equilibrium if the macroscopic variables that characterize the system do not change with time.
Macroscopic Variables Include:
- Pressure (P)
- Volume (V)
- Temperature (T)
- Mass
- Composition
Example
Consider a gas enclosed in a closed, rigid container that is completely insulated from its surroundings. If its pressure, volume, temperature, mass, and composition remain constant with time, the gas is said to be in a state of thermodynamic equilibrium.
2. Influence of Boundary Walls
Whether a system can reach equilibrium with another system depends entirely on the nature of the wall separating them.
A. Adiabatic Walls (Insulating Boundary)
Definition
An adiabatic wall is an insulating wall (which may be movable) that does not allow the transfer of heat or energy from one system to another.
Experiment
Two gases, System A and System B, are placed next to each other and separated by an adiabatic wall. The entire arrangement is also insulated from the surroundings by adiabatic walls.
Observation
It is found experimentally that any possible pair of values $$ (P_A, V_A) $$ for System A can be in equilibrium with any possible pair of values $$ (P_B, V_B) $$ for System B.
Reason
Since the wall does not permit heat transfer, the two systems remain completely independent. A change in one system does not affect the other.
B. Diathermic Walls (Conducting Boundary)
Definition
A diathermic wall is a conducting wall that allows heat energy to flow freely from one system to another.
Experiment
The adiabatic wall separating System A and System B is replaced by a diathermic wall.
Observation
The macroscopic variables of both systems begin to change spontaneously because heat energy starts flowing between them.
3. Achieving Thermal Equilibrium
The spontaneous changes occurring through a diathermic wall do not continue forever.
Step 1: State of Balance
After some time, the spontaneous changes stop and there is no more net energy flow from one system to the other.
Step 2: New Stable States
System A reaches a new stable state:
$$ (P'_A, V'_A) $$
System B reaches a new stable state:
$$ (P'_B, V'_B) $$
Step 3: Thermal Equilibrium
At this stage, System A is in thermal equilibrium with System B.
Core Characteristic of Thermal Equilibrium
The physical condition that defines thermal equilibrium is:
In thermal equilibrium, the temperatures of the two systems are equal.
$$ T_A = T_B $$
where:
- TA = Temperature of System A
- TB = Temperature of System B
When the temperatures become equal, there is no net heat flow between the systems.
Key Points
- Mechanical equilibrium requires zero net external force and zero net torque.
- Thermodynamic equilibrium means all macroscopic variables remain constant with time.
- Adiabatic walls do not allow heat transfer between systems.
- Diathermic walls allow heat transfer between systems.
- Heat transfer through a diathermic wall causes spontaneous changes in both systems.
- Thermal equilibrium is reached when these changes stop.
- The condition for thermal equilibrium is:
$$ T_A = T_B $$
FAQ
1. What is thermodynamic equilibrium?
A state in which the macroscopic variables of a system remain constant with time.
2. What are macroscopic variables?
Pressure, volume, temperature, mass, and composition.
3. What is an adiabatic wall?
An insulating wall that does not allow heat transfer between systems.
4. What is a diathermic wall?
A conducting wall that allows heat transfer between systems.
5. Why do the variables change when a diathermic wall is used?
Because heat energy flows between the systems until thermal equilibrium is established.
6. What is thermal equilibrium?
A state in which two systems have equal temperatures and no net heat transfer occurs between them.
7. What is the condition for thermal equilibrium?
$$ T_A = T_B $$
Quiz
1. A system is in thermodynamic equilibrium when:
- A. Temperature changes continuously
- B. Pressure alone remains constant
- C. Macroscopic variables do not change with time
- D. Heat transfer is maximum
Answer: C. Macroscopic variables do not change with time
2. An adiabatic wall:
- A. Allows heat transfer
- B. Prevents heat transfer
- C. Increases temperature
- D. Decreases pressure
Answer: B. Prevents heat transfer
3. A diathermic wall:
- A. Prevents energy transfer
- B. Prevents temperature change
- C. Allows heat transfer
- D. Prevents equilibrium
Answer: C. Allows heat transfer
4. Thermal equilibrium is achieved when:
- A. Pressure becomes zero
- B. Volume becomes constant
- C. Heat flow stops between systems
- D. Mass becomes equal
Answer: C. Heat flow stops between systems
5. The condition for thermal equilibrium is:
- A. $$P_A = P_B$$
- B. $$V_A = V_B$$
- C. $$T_A = T_B$$
- D. Equal masses
Answer: C. $$T_A = T_B$$
6. In thermal equilibrium, the net heat flow between systems is:
- A. Maximum
- B. Minimum
- C. Infinite
- D. Zero
Answer: D. Zero
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