Final answer:
To convert 10 psia to inches of mercury vacuum, we first calculate the gauge pressure by subtracting atmospheric pressure and then convert the result to inches of mercury. The approximate vacuum pressure is -9.57 inches Hg Vac.
Step-by-step explanation:
To convert 10 psia (pounds per square inch absolute) to inches of mercury vacuum (inches Hg Vac), we need to know the relationship between these two units of pressure. We will use the relationship that 1 atm equals 760 mmHg, which is the same as 29.92 inches Hg. As 1 psi is equivalent to 2.036 inches Hg (by dividing 29.92 by 14.7), we can convert 10 psia to inches Hg. First, we need to find the pressure in psia relative to atmospheric pressure (also known as gauge pressure) and then convert this to inches Hg. Since atmospheric pressure is 14.7 psia, the gauge pressure is 10 psia - 14.7 psia = -4.7 psia. Multiply -4.7 psi by 2.036 inches Hg/psi to get the pressure in inches Hg Vac. The result is a vacuum of approximately -9.57 inches of mercury (inches Hg Vac).