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An isotherm is a collection of points that are all at the same temperature. If two (different) isotherms were to touch each other then that would imply that they were at the same temperature but, by definition, if they have points on them at different temperatures then all the points on them must be at different temperatures.

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No. Two isotherms have different temperatures. If they intersected, the intersection point would have two temperatures at once, which is not possible.

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Q: Can two isotherm intersect each other?
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