A system X is neither in thermal equilibrium with Y nor with Z. The systems Y and Z

Answer

To solve the question, we need to apply the principles of thermal equilibrium as described by the Zeroth Law of Thermodynamics. Let's break down the solution step by step.

### Step 1: Understand the Zeroth Law of Thermodynamics
The Zeroth Law states that if two systems (let's call them Y and Z) are each in thermal equilibrium with a third system (X), then Y and Z are also in thermal equilibrium with each other. This means their temperatures must be equal.

### Step 2: Analyze the Given Information
The question states that system X is neither in thermal equilibrium with Y nor with Z. This implies:
- The temperature of X (TX) is not equal to the temperature of Y (TY).
- The temperature of X (TX) is not equal to the temperature of Z (TZ).

### Step 3: Determine the Relationship Between Y and Z
Since X is not in thermal equilibrium with either Y or Z, we cannot directly infer the relationship between Y and Z based solely on the information about X. The temperatures of Y and Z could be:
- Equal (TY = TZ)
- Y could be hotter than Z (TY > TZ)
- Y could be cooler than Z (TY < TZ)

### Step 4: Conclusion
Since we have established that Y and Z can have any of the three relationships with respect to each other, we conclude that:
- The systems Y and Z may or may not be in thermal equilibrium with each other.

Thus, the correct answer is option C: "may be in thermal equilibrium."