Question

The gauge pressure of the air in an automobile tire is 32 lb/in \(^{2}\). Convert this to (a) \(\mathrm{Pa},\) (b) torr, \((\mathrm{c})\) atm.

Short answer

Answer: The equivalent pressure values for 32 lb/in² gauge pressure are approximately 322058.092 Pa, 2415.68 torr, and 3.178 atm.

Step-by-step solution

Convert gauge pressure to absolute pressure

Since atmospheric pressure is approximately 14.7 lb/in², and the given pressure is gauge pressure, to find the absolute pressure, we need to add atmospheric pressure to the gauge pressure. Absolute Pressure = Gauge Pressure + Atmospheric Pressure Absolute Pressure = 32 lb/in² + 14.7 lb/in² Absolute Pressure = 46.7 lb/in²

Convert from lb/in² to Pa (Pascal)

To convert from lb/in² to Pa, we will use the following conversion factor: 1 lb/in² = 6894.76 Pa. Absolute Pressure in Pa = Absolute Pressure in lb/in² × conversion factor Pressure in Pa = 46.7 lb/in² * 6894.76 Pa Pressure in Pa = 322058.092 Pa

Convert from lb/in² to torr

To convert from lb/in² to torr, we first need to convert from lb/in² to atm, and then from atm to torr using the following conversion factors: 1 lb/in² = 0.06804596 atm 1 atm = 760 torr Absolute Pressure in atm = Absolute Pressure in lb/in² × conversion factor Pressure in atm = 46.7 lb/in² * 0.06804596 atm Pressure in atm ≈ 3.178 atm Now, convert to torr: Pressure in torr = Pressure in atm × conversion factor Pressure in torr = 3.178 atm * 760 torr Pressure in torr ≈ 2415.68 torr

Convert from lb/in² to atm (atmosphere)

We have already found the conversion of lb/in² to atm in step 3. Pressure in atm ≈ 3.178 atm

Presenting the final results

The pressure in different units is: (a) Pa: 322058.092 Pa (b) torr: 2415.68 torr (c) atm: 3.178 atm