I dislike these kinds of questions, because they’re usually posed at a point well before the wave equations are presented. At this point, you are largely working with verbal explanations and, as you point out, verbal explanations are much harder to pin down.
I agree that they’re not great test questions, but they can be excellent class discussion or homework problem set questions (as long as you encourage working together on homework, which can work in college but not usually in high school). If anything, using them well puts a much higher burden of understanding on the teacher to not only know the answer but also all the ways students are likely to go wrong in trying to reason about the answer and how to steer the discussion without just giving the answer.
In this case, yeah, I’m sure this question was posed at a point where the student doesn’t really know what T and P mean at a fundamental level, what makes a gas “ideal,” what the Maxwell-Boltzmann velocity distribution is and why, and a whole bunch of other relevant things. Given that, you should still be able to reason it out using dimensional analysis, the definition of kinetic energy, the idea that T is proportional to kinetic energy, and looking at some limiting cases and boundary conditions, but it isn’t easy.
I agree that they’re not great test questions, but they can be excellent class discussion or homework problem set questions (as long as you encourage working together on homework, which can work in college but not usually in high school). If anything, using them well puts a much higher burden of understanding on the teacher to not only know the answer but also all the ways students are likely to go wrong in trying to reason about the answer and how to steer the discussion without just giving the answer.
In this case, yeah, I’m sure this question was posed at a point where the student doesn’t really know what T and P mean at a fundamental level, what makes a gas “ideal,” what the Maxwell-Boltzmann velocity distribution is and why, and a whole bunch of other relevant things. Given that, you should still be able to reason it out using dimensional analysis, the definition of kinetic energy, the idea that T is proportional to kinetic energy, and looking at some limiting cases and boundary conditions, but it isn’t easy.