Tell me please if there is any difference between the following sentences?
I can't go for a break as I have to prepare the classroom for the follow-up students.
I can't go for a break as I have to prepare the classroom for the next students.
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In your given context, "follow-up" sounds wrong.
Normally, when using "next" to refer to a succession of people it means different people. For example, a classroom may be used for a class of students, and then the next class comes in - a completely different set of students.
"Follow-up" normally refers to continuing situations where the same person or thing is involved in a sequence of events or appointments. For example, if a doctor sees a patient and determines that they need to come back for further treatment the next appointment may be called a "follow-up" appointment.
I think you may have mixed up "follow-up" with "the following", which can be used interchangeably with "next" in your context, although it sounds more natural when used with "class" than "students":
I can't go for a break as I have to prepare the classroom for the following class.