Increase of temperature of an ideal nondegenerate quantum gas in a suddenly expanding box due to energy quantization

We show that due to energy quantization the temperature of an ideal nondegenerate quantum gas in a rectangular box always increases after a sudden expansion of the box and a subsequent thermalization. The maximal increment of temperature is proportional to the square root of the product of the initial absolute temperature by the energy of the first discrete quantum level, i.e., it is proportional to the first power of the Planck constant.