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Chapter 11: Problem 23

A weather forecaster reports the barometric pressure as \(29.7\) inches of mercury. \([1 \mathrm{in.}=2.54 \mathrm{~cm}]\) (a) How many millimeters of mercury is this? (b) How many atmospheres is this?

Short Answer

Expert verified
(a) The barometric pressure is equal to 754.38 mm of mercury. (b) The barometric pressure in atmospheres is approximately 0.992 atm.

Step by step solution

01

(a) Conversion of barometric pressure from inches to millimeters

To convert the given pressure from inches to millimeters, we need to first convert inches to centimeters and then centimeters to millimeters. We are given the conversion factor 1 inch = 2.54 cm. We know that 1 cm = 10 mm. Given pressure, P = 29.7 inches Now let us perform the conversion: 1. Convert inches to centimeters (\(2.54 \,cm = 1 \,inch\)) 2. Convert centimeters to millimeters (\(1 \,cm = 10 \,mm\)) \[ P_{cm} = 29.7 in \times \frac{2.54 \,cm}{1 \,inch} = 75.438 \,cm \] \[ P_{mm} = 75.438 \, cm \times \frac{10 \,mm}{1 \,cm} = 754.38 \, mm \] So, the reported barometric pressure is equal to 754.38 mm of mercury.
02

(b) Conversion of barometric pressure into atmospheres

To convert the pressure we just calculated in millimeters of mercury into atmospheres, we need to use the standard conversion factor: \(1 \,atm = 760 \,mm\, Hg\) We have the pressure in mm of mercury, \(P_{mm} = 754.38 \, mm\, Hg\) So, let's convert mm of mercury into atmospheres by using the given conversion factor: \[ P_{atm} = P_{mm} \times \frac{1 \,atm}{760\,mm\,Hg} = 754.38 \, mm\,Hg \times \frac{1 \,atm}{760 \,mm\, Hg} = 0.992345\, atm \] Therefore, the barometric pressure in atmospheres is approximately 0.992 atm.

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