Question

The vacuum pressure of a condenser is given to be 80 kPa. If the atmospheric pressure is \(98 \mathrm{kPa}\), what is the gage pressure and absolute pressure in \(\mathrm{kPa}, \mathrm{kN} / \mathrm{m}^{2}, \mathrm{lbf} / \mathrm{in}^{2}\) psi, and mmHg.

Short answer

Question: Find the gage pressure and absolute pressure in kPa, kN/m², lbf/in² (psi), and mmHg given the vacuum pressure is 80 kPa and the atmospheric pressure is 98 kPa. Answer: Gage Pressure: - 18 kPa - 18 kN/m² - 2.611 psi - 135.011 mmHg Absolute Pressure: - 80 kPa - 80 kN/m² - 11.604 psi - 600.050 mmHg

Step-by-step solution

Calculate the gage pressure

To calculate the gage pressure, we will subtract the vacuum pressure from the atmospheric pressure: Gage pressure = Atmospheric pressure - Vacuum pressure = \(98\,\text{kPa} - 80\,\text{kPa} = 18\,\text{kPa}\).

Determine the absolute pressure

Because we are given the vacuum pressure, it is already in absolute terms, so: Absolute pressure = Vacuum pressure = \(80\,\text{kPa}\).

Convert pressures into various units

First, we will convert the gage pressure and absolute pressure from kPa to kN/m², which happens to be a direct 1:1 conversion: Gage pressure = \(18\,\text{kPa} = 18\,\text{kN/m}^2\), Absolute pressure = \(80\,\text{kPa} = 80\,\text{kN/m}^2\). Next, we will convert the gage pressure and absolute pressure from kPa to lbf/in² (psi) by using the conversion factor \(1\,\text{kPa} = 0.145037737\,\text{psi}\): Gage pressure = \(18\,\text{kPa} * 0.145037737 = 2.611\,\text{psi}\), Absolute pressure = \(80\,\text{kPa} * 0.145037737 = 11.604\,\text{psi}\). Now, we will convert the gage pressure and absolute pressure from kPa to mmHg, considering that \(1\,\text{kPa} = 7.50062\,\text{mmHg}\): Gage pressure = \(18\,\text{kPa} * 7.50062 = 135.011\,\text{mmHg}\), Absolute pressure = \(80\,\text{kPa} * 7.50062 = 600.050\,\text{mmHg}\). In summary, the gage pressure and absolute pressure in different units are as follows: Gage Pressure: \(18\,\text{kPa}\), \(18\,\text{kN/m}^2\), \(2.611\,\text{psi}\), \(135.011\,\text{mmHg}\). Absolute Pressure: \(80\,\text{kPa}\), \(80\,\text{kN/m}^2\), \(11.604\,\text{psi}\), \(600.050\,\text{mmHg}\).