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Chapter 9: Problem 21

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

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

Step by step solution

01

Convert gauge pressure to absolute pressure

Since atmospheric pressure is approximately 14.7 lb/in虏, 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/in虏 + 14.7 lb/in虏 Absolute Pressure = 46.7 lb/in虏
02

Convert from lb/in虏 to Pa (Pascal)

To convert from lb/in虏 to Pa, we will use the following conversion factor: 1 lb/in虏 = 6894.76 Pa. Absolute Pressure in Pa = Absolute Pressure in lb/in虏 脳 conversion factor Pressure in Pa = 46.7 lb/in虏 * 6894.76 Pa Pressure in Pa = 322058.092 Pa
03

Convert from lb/in虏 to torr

To convert from lb/in虏 to torr, we first need to convert from lb/in虏 to atm, and then from atm to torr using the following conversion factors: 1 lb/in虏 = 0.06804596 atm 1 atm = 760 torr Absolute Pressure in atm = Absolute Pressure in lb/in虏 脳 conversion factor Pressure in atm = 46.7 lb/in虏 * 0.06804596 atm Pressure in atm 鈮� 3.178 atm Now, convert to torr: Pressure in torr = Pressure in atm 脳 conversion factor Pressure in torr = 3.178 atm * 760 torr Pressure in torr 鈮� 2415.68 torr
04

Convert from lb/in虏 to atm (atmosphere)

We have already found the conversion of lb/in虏 to atm in step 3. Pressure in atm 鈮� 3.178 atm
05

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

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