Question

converting between pressure units

1. the pressure in denver, colorado (elevation 5280 ft), averages about 24.9 in hg. convert this pressure to each indicated unit.

missed this? read section 6.2
a. atm
b. mmhg
c. psi
d. pa

Explanation:

Step1: Recall pressure conversion factors

We know the following conversion factors:

• 1 atm = 760 mmHg = 760 torr = 14.696 psi = \(1.01325\times10^{5}\) Pa
• 1 in Hg = 25.4 mmHg (since 1 inch = 25.4 mm, and pressure in mmHg is based on height of Hg column, so 1 in Hg = 25.4 mmHg)
• Also, 1 in Hg = \(\frac{1}{2.036}\) atm (approx), 1 in Hg = \(\frac{14.696}{29.92}\) psi (approx, since 29.92 in Hg = 1 atm = 14.696 psi), and 1 in Hg = \(3386.39\) Pa (derived from 1 mmHg = 133.322 Pa, so 25.4 mmHg/in Hg * 133.322 Pa/mmHg = 3386.39 Pa/in Hg)

Step2: Convert 24.9 in Hg to atm (part a)

Using the conversion factor \(1\) atm \( = 29.92\) in Hg (approximate value for standard atmosphere). So the formula to convert in Hg to atm is \(\text{Pressure (atm)}=\frac{\text{Pressure (in Hg)}}{29.92}\)
Substitute \(\text{Pressure (in Hg)} = 24.9\)
\(\text{Pressure (atm)}=\frac{24.9}{29.92}\approx0.832\) atm

Step3: Convert 24.9 in Hg to mmHg (part b)

Using the conversion factor \(1\) in Hg \( = 25.4\) mmHg. So the formula is \(\text{Pressure (mmHg)}=\text{Pressure (in Hg)}\times25.4\)
Substitute \(\text{Pressure (in Hg)} = 24.9\)
\(\text{Pressure (mmHg)} = 24.9\times25.4 = 24.9\times25 + 24.9\times0.4=622.5+9.96 = 632.46\) mmHg (exact value) or using \(1\) atm \( = 760\) mmHg and \(1\) atm \( = 29.92\) in Hg, we can also calculate as \(\frac{24.9}{29.92}\times760\approx632\) mmHg (approximate, slight difference due to rounding of 29.92)

Step4: Convert 24.9 in Hg to psi (part c)

Using the conversion factor \(1\) atm \( = 14.696\) psi and \(1\) atm \( = 29.92\) in Hg. So first find the pressure in atm (from step 2: \(\approx0.832\) atm) and then convert to psi. The formula is \(\text{Pressure (psi)}=\text{Pressure (atm)}\times14.696\)
Or using the direct conversion: \(1\) in Hg \(=\frac{14.696}{29.92}\) psi \(\approx0.4912\) psi/in Hg
So \(\text{Pressure (psi)} = 24.9\times0.4912\approx12.23\) psi

Step5: Convert 24.9 in Hg to Pa (part d)

Using the conversion factor \(1\) in Hg \( = 3386.39\) Pa (as derived earlier). So the formula is \(\text{Pressure (Pa)}=\text{Pressure (in Hg)}\times3386.39\)
Substitute \(\text{Pressure (in Hg)} = 24.9\)
\(\text{Pressure (Pa)} = 24.9\times3386.39\approx24.9\times3386 = 24\times3386+0.9\times3386 = 81264 + 3047.4=84311.4\) Pa (approximate, more accurately \(24.9\times3386.39 = 84321.11\) Pa)

Answer:

s (for each part):
a. \(\approx\boldsymbol{0.832}\) atm
b. \(\boldsymbol{632.46}\) mmHg (or \(\approx632\) mmHg)
c. \(\approx\boldsymbol{12.23}\) psi
d. \(\approx\boldsymbol{8.43\times10^{4}}\) Pa (or \(\approx84321\) Pa)