2 psia is equivalent to
a. $29^{\circ} Hg$
b. $27^{\circ} Hg$
c. $26^{\circ} itg$
d. $28^{\circ} Hg
Answer (2)
Set up a proportion using the relationship between psia and inches of mercury: in . H g p s ia = 29.92 14.7 .
Substitute the given value of 2 psia into the proportion: x 2 = 29.92 14.7 .
Solve for x to find the equivalent pressure in inches of mercury: x = 14.7 2 × 29.92 ≈ 4.0707 .
Since none of the options are close to the calculated value, and there seems to be a typo in the options, there is no correct answer among the provided choices.
Explanation
Problem Analysis We are given a pressure of 2 psia (pounds per square inch absolute) and asked to find the equivalent pressure in inches of mercury (in. Hg). We know that standard atmospheric pressure is 14.7 psia, which is equivalent to 29.92 in. Hg. We can use this information to convert 2 psia to inches of mercury.
Setting up the Proportion To convert psia to inches of mercury, we can set up a proportion using the known relationship between standard atmospheric pressure in both units:
in . H g p s ia = 29.92 14.7
We want to find the equivalent pressure in inches of mercury for 2 psia. Let x be the pressure in inches of mercury. Then we have:
x 2 = 29.92 14.7
To solve for x , we can cross-multiply:
14.7 x = 2 × 29.92
x = 14.7 2 × 29.92
Calculating the Equivalent Pressure Now, we calculate the value of x :
x = 14.7 2 × 29.92 = 14.7 59.84 ≈ 4.0707
Rounding the result to the nearest whole number, we get 4.
Comparing with the Options The calculated value is approximately 4 in. Hg. Comparing this to the given options, we see that none of the options are close to 4. However, there seems to be a typo in the options, as they include a degree symbol ( ∘ ) which is not appropriate for units of pressure. Assuming the options are meant to be in inches of mercury, and given the choices, it is likely there was a mistake in the problem statement or the provided options. However, based on our calculation, the closest answer would be approximately 4 in. Hg. Since none of the options are close to the calculated value, we should double-check the initial information and the question itself. However, assuming the question is correct as is, there is no correct answer among the provided choices.
Final Answer Since the options provided seem to have a typo and none of them are close to the calculated value of approximately 4 in. Hg, it's likely there's an error in the question or the options. However, based on the conversion, 2 psia is approximately 4 in. Hg.
Examples
Understanding pressure conversions is crucial in many real-world applications. For example, in meteorology, atmospheric pressure is measured in inches of mercury (in. Hg) or millibars. Converting between different units of pressure, such as pounds per square inch (psi) and inches of mercury, allows scientists and engineers to compare and analyze data from various sources. This is also important in fields like aviation, where pilots need to understand pressure readings to ensure safe flight operations. Similarly, in scuba diving, knowing the pressure at different depths is essential for calculating decompression stops and avoiding decompression sickness.
The conversion from 2 psia to inches of mercury is approximately 4.07 in. Hg. None of the provided options are correct due to an apparent typographical error. Therefore, there is no accurate answer among the given choices.
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