A system of (N) spins at a negative temperature ((E>0)) is brought into contact with an ideal-gas

Question:

A system of $N$ spins at a negative temperature $(E>0)$ is brought into contact with an ideal-gas thermometer consisting of $N^{\prime}$ molecules. What will the nature of their state of mutual equilibrium be? Will their common temperature be negative or positive, and in what manner will it be affected by the ratio $N^{\prime} / N$ ?

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