1. **State the problem:** Convert the given pressure readings to kPa absolute, assuming the barometer reads 29.92 in. Hg (which is standard atmospheric pressure). 2. **Important formulas and conversions:** - Atmospheric pressure $P_{atm} = 29.92$ in. Hg - 1 in. Hg = 3.38639 kPa - 1 cm Hg = 0.133322 kPa - 1 psi = 6.89476 kPa - Absolute pressure $P_{abs} = P_{atm} + P_{gage}$ for gage pressures - For vacuum pressures, $P_{abs} = P_{atm} - P_{vacuum}$ --- ### a. Convert 85 cm Hg gage to kPa absolute 3. Convert 85 cm Hg gage to kPa gage: $$85 \text{ cm Hg} \times 0.133322 \frac{\text{kPa}}{\text{cm Hg}} = 11.33237 \text{ kPa (gage)}$$ 4. Convert atmospheric pressure to kPa: $$29.92 \text{ in. Hg} \times 3.38639 \frac{\text{kPa}}{\text{in. Hg}} = 101.325 \text{ kPa}$$ 5. Calculate absolute pressure: $$P_{abs} = P_{atm} + P_{gage} = 101.325 + 11.33237 = 112.65737 \text{ kPa}$$ --- ### b. Convert 12.85 psi vacuum to kPa absolute 6. Convert vacuum pressure to kPa: $$12.85 \text{ psi} \times 6.89476 \frac{\text{kPa}}{\text{psi}} = 88.5651 \text{ kPa (vacuum)}$$ 7. Calculate absolute pressure: $$P_{abs} = P_{atm} - P_{vacuum} = 101.325 - 88.5651 = 12.7599 \text{ kPa}$$ --- ### c. Convert 38 in. Hg gage to kPa absolute 8. Convert 38 in. Hg gage to kPa gage: $$38 \text{ in. Hg} \times 3.38639 \frac{\text{kPa}}{\text{in. Hg}} = 128.67382 \text{ kPa (gage)}$$ 9. Calculate absolute pressure: $$P_{abs} = P_{atm} + P_{gage} = 101.325 + 128.67382 = 229.99882 \text{ kPa}$$ --- **Final answers:** - a. 112.66 kPa absolute - b. 12.76 kPa absolute - c. 230.00 kPa absolute