Final answer:
The approximate absolute pressure when the barometric pressure is 760 mm Hg and the vacuum gauge indicates 500 mm Hg is 1260 mm Hg. This is found by adding the atmospheric pressure to the gauge pressure.
Step-by-step explanation:
When the barometric pressure is 760 mm Hg and a vacuum gauge indicates 500 mm Hg, to find the approximate absolute pressure, we must add the gauge pressure to the atmospheric pressure.
The formula to calculate the absolute pressure (Pabs) is Pabs = Patm + Pgauge, where Patm is the atmospheric pressure and Pgauge is the gauge pressure.
Since the atmospheric pressure is given as 760 mm Hg (which is equivalent to 1 atm due to the average atmospheric pressure at sea level) and the gauge pressure is 500 mm Hg, we calculate the absolute pressure as follows:
760 mm Hg (atmospheric pressure) + 500 mm Hg (gauge pressure)
= 1260 mm Hg (absolute pressure).
Therefore, the approximate absolute pressure corresponding to the gauge reading is 1260 mm Hg.