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Ch 18: A Macroscopic Description of Matter
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
Chapter 18, Problem 44a

The semiconductor industry manufactures integrated circuits in large vacuum chambers where the pressure is 1.0×10-10 mm of Hg. What fraction is this of atmospheric pressure?

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1
Convert the given pressure in the vacuum chamber from mm of Hg to Pascals (Pa) using the conversion factor: 1 mm of Hg = 133.322 Pa. The pressure in the vacuum chamber is \( P_{vacuum} = 1.0 \times 10^{-10} \times 133.322 \) Pa.
Determine the atmospheric pressure in Pascals. Standard atmospheric pressure is \( P_{atm} = 101325 \) Pa.
Calculate the fraction of the vacuum chamber pressure to atmospheric pressure using the formula: \( \text{Fraction} = \frac{P_{vacuum}}{P_{atm}} \).
Substitute the values of \( P_{vacuum} \) and \( P_{atm} \) into the formula to compute the fraction.
Express the result as a dimensionless number, which represents the fraction of the vacuum chamber pressure relative to atmospheric pressure.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Atmospheric Pressure

Atmospheric pressure is the force exerted by the weight of air above a given point, typically measured at sea level as approximately 1013.25 hPa (hectopascals) or 760 mm of Hg (millimeters of mercury). Understanding this baseline pressure is crucial for comparing other pressures, such as those found in vacuum chambers.
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Vacuum Pressure

Vacuum pressure refers to the pressure in a system that is lower than atmospheric pressure. It is often expressed in terms of mm of Hg or torr, where a perfect vacuum is 0 mm of Hg. In the context of the semiconductor industry, achieving a high vacuum (like 1.0×10^−10 mm of Hg) is essential for processes like deposition and etching, which require minimal contamination.
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Pressure Ratio Calculation

Calculating the fraction of a given pressure relative to atmospheric pressure involves dividing the pressure in question by the standard atmospheric pressure. This ratio helps quantify how much lower the vacuum pressure is compared to normal conditions, providing insight into the effectiveness of the vacuum system used in manufacturing processes.
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Related Practice
Textbook Question

A 6.0-cm-diameter, 10-cm-long cylinder contains 100 mg of oxygen (O₂) at a pressure less than 1 atm. The cap on one end of the cylinder is held in place only by the pressure of the air. One day when the atmospheric pressure is 100 kPa, it takes a 184 N force to pull the cap off. What is the temperature of the gas?

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The semiconductor industry manufactures integrated circuits in large vacuum chambers where the pressure is 1.0×10-10 mm of Hg. At T=20°C, how many molecules are in a cylindrical chamber 40 cm in diameter and 30 cm tall?

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