Two system in thermal equilibrium with a third system separately are in thermal equilibrium with each other. The above statement is

Options

A. First law of thermaodynamics
B. Second law of thermodynamics
C. Third law of thermodynamics
D. Zeroth law of thermodynamics

Explanation

To solve the question regarding the thermal equilibrium of two systems with a third system, we can break it down step by step.

### Step-by-Step Solution:

1. **Understanding Thermal Equilibrium**:
- Thermal equilibrium occurs when two systems are at the same temperature and there is no net flow of thermal energy between them.

2. **Identifying the Systems**:
- Let's denote the systems as A, B, and C.
- According to the question, systems A and B are each in thermal equilibrium with a third system C.

3. **Applying the Concept of Thermal Equilibrium**:
- If system A is in thermal equilibrium with system C, it means that their temperatures are equal (T_A = T_C).
- Similarly, if system B is in thermal equilibrium with system C, then T_B = T_C.

4. **Concluding the Relationship**:
- Since both A and B are in thermal equilibrium with C, and both have the same temperature as C, we can conclude that T_A = T_B.
- Therefore, systems A and B must also be in thermal equilibrium with each other.

5. **Identifying the Law**:
- This principle is known as the Zeroth Law of Thermodynamics, which states that if two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other.

6. **Final Answer**:
- The statement provided in the question is an expression of the Zeroth Law of Thermodynamics.

### Conclusion:
- The correct answer to the question is **Zeroth Law of Thermodynamics**.

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