The area under the Maxwell-Boltzmann distribution curve represents the total number of molecules (N) in the system. The problem states we are comparing the same sample of gas at two different temperatures. While the shape of the curve flattens and broadens at higher temperatures, the total count of molecules does not change. Therefore, the area under both curves must be identical.
This question tests whether students confuse the distribution of energy with the required threshold .
Here are some mathematical representations of the Maxwell-Boltzmann distribution: