question_answer 31)

                    Mark the correct option:                 (a) A system X is in thermal equilibrium with Y but not with Z. System Y and Z may be in thermal equilibrium with each other.                 (b) A system X is in thermal equilibrium with Y but not with Z. Systems Y and Z are not in thermal equilibrium with each other.                 (c)  A system X is neither in thermal equilibrium with Y nor with Z. The systems Y and Z must be in thermal equilibrium with each other.                 (d) A system X is neither in thermal equilibrium with Y nor with Z. The system Y and Z may be in thermal equilibrium with each other.                

Answer:

                  (b, a) (a) \[{{T}_{X}}={{T}_{Y}}\]  and \[{{T}_{x}}\ne {{T}_{z}}\] \[\therefore {{T}_{Y}}\ne ~Tz\]                 (b) \[{{T}_{X}}={{T}_{Y}}\] and \[{{T}_{X}}\ne \,{{T}_{Z}}\therefore \,{{T}_{Y}}\ne \,{{T}_{Z}}\]                 (c) \[{{T}_{X}}\ne {{T}_{Y}}\] and \[{{T}_{X}}\ne \,{{T}_{Z}}\therefore \,{{T}_{Y}}\ne \,{{T}_{Z}}\]                 (d) \[{{T}_{X}}\ne {{T}_{Y}}\] and \[{{T}_{X}}\ne \,{{T}_{Z}}\therefore \,{{T}_{Y}}\] may be equal \[{{T}_{Z}}\].