We improved the sensitivity of existing commercial Pirani-vacuum gauges employing the AC method in the vacuum range above 1 Torr. The signals obtained through the use of the AC method yield information related to the specific heat and heat conductivity of gas. The output signal is obtained by two components: the oscillating temperature amplitude, and its phase. The amplitude increases with the decrease of pressure in the vacuum range from the atmosphere to about 1 Torr, which arises from the decrease of the heat capacity with the decrease of gas density. In contrast, the phase decreases monotonically as pressure decreases and the slop of a dΘ/d(log P) is large at higher than 1 Torr. This provides a good advantage for developing a new Pirani gauge with high sensitivity.