If a body A is in thermal equilibrium with three different bodies B, C and D then

Options

A. B is in thermal equilibrium with C
B. C is in thermal equilibrium with D
C. D is in thermal equilibrium with B
D. All of these

Answer

To solve the question, we need to apply the concept of thermal equilibrium as stated in the Zeroth Law of Thermodynamics. Here’s the step-by-step solution:

### Step 1: Understand Thermal Equilibrium
Thermal equilibrium occurs when two bodies are at the same temperature and there is no net heat transfer between them. According to the Zeroth Law of Thermodynamics, if body A is in thermal equilibrium with body B, and body B is in thermal equilibrium with body C, then body A must also be in thermal equilibrium with body C.

### Step 2: Analyze the Given Information
We are given that body A is in thermal equilibrium with three different bodies: B, C, and D. This means:
- A is in thermal equilibrium with B (A ≈ B)
- A is in thermal equilibrium with C (A ≈ C)
- A is in thermal equilibrium with D (A ≈ D)

### Step 3: Apply the Zeroth Law
Since A is in thermal equilibrium with B, C, and D, we can apply the Zeroth Law:
1. Since A ≈ B and A ≈ C, it follows that B ≈ C.
2. Since A ≈ B and A ≈ D, it follows that B ≈ D.
3. Since A ≈ C and A ≈ D, it follows that C ≈ D.

### Step 4: Conclusion
From the above deductions, we can conclude:
- B is in thermal equilibrium with C (B ≈ C)
- C is in thermal equilibrium with D (C ≈ D)
- D is in thermal equilibrium with B (D ≈ B)

Thus, all pairs (B, C), (C, D), and (D, B) are in thermal equilibrium.

### Final Answer
The correct option is "all of these."

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