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Using the zeroth law of thermodynamics, identify the CORRECT statement(s) among the following: (A) X is in thermal equilibrium with Y but not with Z; Y and Z may be in thermal equilibrium with each other. (B) X is in thermal equilibrium with Y but not with Z; Y and Z are not in thermal equilibrium with each other. (C) X is in equilibrium with neither Y nor Z; Y and Z must be in thermal equilibrium with each other. (D) X is in equilibrium with neither Y nor Z; Y and Z may be in thermal equilibrium with each other.

1. X is in thermal equilibrium with Y but not with Z; Y and Z may be in thermal equilibrium with each other.
2. X is in thermal equilibrium with Y but not with Z; Y and Z are not in thermal equilibrium with each other.
3. X is in equilibrium with neither Y nor Z; Y and Z must be in thermal equilibrium with each other.
4. X is in equilibrium with neither Y nor Z; Y and Z may be in thermal equilibrium with each other.

Correct answer: X is in thermal equilibrium with Y but not with Z; Y and Z are not in thermal equilibrium with each other.

Solution

If X is in equilibrium with Y (same temperature) but not with Z, then Y and Z cannot be at the same temperature, so they are NOT in equilibrium (B correct). When X equals neither, Y and Z may or may not be equal, so (D) is also acceptable while (C) is wrong.

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