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

Explanation

To solve the problem, we need to understand the concept of thermal equilibrium and the implications of the Zeroth Law of Thermodynamics. Here’s the step-by-step solution:

### Step 1: Understanding Thermal Equilibrium
When two bodies are in thermal equilibrium, it means that there is no net heat exchange between them. This occurs when both bodies are at the same temperature.

### Step 2: Analyzing Body A
Given that body A is in thermal equilibrium with bodies B, C, and D, we can conclude:
- The temperature of A (T_A) is equal to the temperature of B (T_B).
- The temperature of A (T_A) is equal to the temperature of C (T_C).
- The temperature of A (T_A) is equal to the temperature of D (T_D).

This can be summarized as:
\[ T_A = T_B = T_C = T_D \]

### Step 3: Applying the Zeroth Law of Thermodynamics
According to the Zeroth Law of Thermodynamics:
- If body A is in thermal equilibrium with body B, and body A is also in thermal equilibrium with body C, then body B must be in thermal equilibrium with body C.

From our earlier conclusion:
- Since \( T_A = T_B \) and \( T_A = T_C \), we can deduce that \( T_B = T_C \).
- Similarly, since \( T_A = T_B \) and \( T_A = T_D \), we can conclude that \( T_B = T_D \) and \( T_C = T_D \).

### Step 4: Conclusion
Thus, we can conclude that:
- Body B is in thermal equilibrium with body C.
- Body C is in thermal equilibrium with body D.
- Body D is in thermal equilibrium with body B.

Therefore, all bodies A, B, C, and D are in thermal equilibrium with each other.

### Final Answer
The correct conclusion is that all bodies A, B, C, and D are in thermal equilibrium, which corresponds to the option stating "all of these."

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