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Q.61

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 386

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Short Answer

The -tall cylinder in FIGURE P14.61 contains air at a pressure of . A very thin, frictionless piston of negligible mass is placed at the top of the cylinder, to prevent any air from escaping, then mercury is slowly poured into the cylinder until no more can be added without the cylinder overflowing. What is the height h of the column of compressed air?

Hint: Boyle's law, which you learned in chemistry, says for a gas compressed at constant temperature, which we will assume to be the case.

Hence, the length of air column is

See the step by step solution

Step by Step Solution

Step :1 Introduction 

The force applied perpendicular to an object's surface per unit area across which that force is spread is known as pressure. The pressure gauged in relation to the ambient pressure is known as gauge pressure. Pressure is measured in a variety of ways. The perpendicular force per unit area, or the tension at a point within a confined fluid, is known as pressure in the physical sciences.

Step :2 Explanation 

An ideal gas obeys Boyle's law. The Boyle's law states that the product of pressure and volume is constant for constant temperature condition. The Boyle's law expression is:

The initial pressure and volume in the column are and . The area of cross section of the cylinder is . The length of the cylinder is . The length of the air column is . The air column will obey Boyle's law.

Step :3 Pressure 

The final pressure is

The final volume is

Apply Boyle's law to the column of gas:

Substitute

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