Convert the following readings of pressureto kPa absolute, assuming that the barometer reads 760mm Hg: (a)90cm Hg gage; (b) 40cm Hg vacuum; (c) 100psig; (d) 8in Hg vacuumand (e) 76 in Hg gage. Thank you very much!

(a) Using the conversion factor $1\text{cm Hg}=0.133322368\text{kPa}$, we have:
$90\text{cm Hg}\times 0.133322368\text{kPa/cm Hg}=12.00091\text{kPa}$
(b) Since it's a vacuum, we need to subtract it from the atmospheric pressure. Atmospheric pressure is $760\text{mm Hg}$, and the conversion factor is $1\text{mm Hg}=0.133322368\text{kPa}$. Therefore:
$(760\text{mm Hg}-40\text{cm Hg})\times 0.133322368\text{kPa/mm Hg}=98.6651\text{kPa}$
(c) Since ''psig'' means ''pounds per square inch gauge,'' we first need to convert it to pounds per square inch absolute (psia). The conversion factor is $1\text{psig}=1\text{psia}+14.696\text{psi}$. Then, we convert psia to kPa using the conversion factor $1\text{psi}=6.89476\text{kPa}$. Therefore:
$100\text{psig}\times (1\text{psia}+14.696\text{psi})\times 6.89476\text{kPa/psi}=829.495\text{kPa}$
(d) Similar to (b), we need to subtract the vacuum from atmospheric pressure. The conversion factor is $1\text{in Hg}=0.0334211\text{kPa}$. Hence:
$(760\text{mm Hg}-8\text{in Hg})\times 0.0334211\text{kPa/in Hg}=23.7434\text{kPa}$
(e) First, we need to convert it to inches Hg absolute (in Hg abs). Since it's a gage reading, we add it to atmospheric pressure. The conversion factor is $1\text{in Hg}=0.0334211\text{kPa}$. Therefore:
$(760\text{mm Hg}+76\text{in Hg})\times 0.0334211\text{kPa/in Hg}=100.7457\text{kPa}$

(a) To convert 90 cm Hg gauge to kPa absolute:
$P_{\text{abs}}=P_{\text{gauge}}+P_{\text{atm}}=90\text{{cm Hg}\}+760\text{{mm Hg}\}$
(b) To convert 40 cm Hg vacuum to kPa absolute:
$P_{\text{abs}}=P_{\text{atm}}-P_{\text{vacuum}}=760\text{{mm Hg}\}-40\text{{cm Hg}\}$
(c) To convert 100 psi gauge to kPa absolute:
$P_{\text{abs}}=P_{\text{gauge}}+P_{\text{atm}}=100\text{{psi}\}+101.325\text{{kPa}\}$
(d) To convert 8 in Hg vacuum to kPa absolute:
$P_{\text{abs}}=P_{\text{atm}}-P_{\text{vacuum}}=101.325\text{{kPa}\}-8\text{{in Hg}\}$
(e) To convert 76 in Hg gauge to kPa absolute:
$P_{\text{abs}}=P_{\text{gauge}}+P_{\text{atm}}=76\text{{in Hg}\}+101.325\text{{kPa}\}$

Step 1:
(a) $90$ cm Hg gauge:
To convert cm Hg gauge to kPa absolute, we need to add the atmospheric pressure to the gauge pressure. The atmospheric pressure is $760$ mm Hg.
First, let's convert cm Hg to mm Hg:
$90\text{cm Hg}=90\times 10\text{mm Hg}=900\text{mm Hg}$
Then, we can convert mm Hg to kPa:
$900\text{mm Hg}=900\times \left(\frac{101.325}{760}\right)\text{kPa}\approx 119.07\text{kPa}$
Therefore, $90$ cm Hg gauge is approximately $119.07$ kPa absolute.
Step 2:
(b) $40$ cm Hg vacuum:
To convert cm Hg vacuum to kPa absolute, we need to subtract the vacuum pressure from the atmospheric pressure. The atmospheric pressure is $760$ mm Hg.
First, let's convert cm Hg to mm Hg:
$40\text{cm Hg}=40\times 10\text{mm Hg}=400\text{mm Hg}$
Then, we can convert mm Hg to kPa:
$400\text{mm Hg}=400\times \left(\frac{101.325}{760}\right)\text{kPa}\approx 53.57\text{kPa}$
Therefore, $40$ cm Hg vacuum is approximately $53.57$ kPa absolute.
Step 3:
(c) $100$ psi gauge:
To convert psi gauge to kPa absolute, we need to add the atmospheric pressure to the gauge pressure. The atmospheric pressure is $14.696$ psi.
Converting psi gauge to psi absolute:
$100\text{psi}+14.696\text{psi}=114.696\text{psi}$
Then, we can convert psi to kPa:
$114.696\text{psi}\times 6.89476\text{kPa/psi}\approx 790.6\text{kPa}$
Therefore, $100$ psi gauge is approximately $790.6$ kPa absolute.
Step 4:
(d) $8$ in Hg vacuum:
To convert in Hg vacuum to kPa absolute, we need to subtract the vacuum pressure from the atmospheric pressure. The atmospheric pressure is $29.921$ in Hg.
Converting in Hg to mm Hg:
$8\text{in Hg}\times 25.4\text{mm Hg/in Hg}=203.2\text{mm Hg}$
Then, we can convert mm Hg to kPa:
$203.2\text{mm Hg}\times \left(\frac{101.325}{760}\right)\text{kPa}\approx 27.16\text{kPa}$
Therefore, $8$ in Hg vacuum is approximately $27.16$ kPa absolute.
Step 5:
(e) $76$ in Hg gauge:
To convert in Hg gauge to kPa absolute, we need to add the atmospheric pressure to the gauge pressure. The atmospheric pressure is $29.921$ in Hg.
Converting in Hg to mm Hg: $76\text{in Hg}\times 25.4\text{mm Hg/in Hg}=1930.4\text{mm Hg}$
Then, we can convert mm Hg to kPa:
$1930.4\text{mm Hg}\times \left(\frac{101.325}{760}\right)\text{kPa}\approx 258.03\text{kPa}$
Therefore, $76$ in Hg gauge is approximately $258.03$ kPa absolute.