Question

True or false? \(1 \mathrm{~atm}=76 \mathrm{~mm} \mathrm{Hg}=760 \mathrm{~cm} \mathrm{Hg}\). If false, fix it.

Short answer

The given relation is false. The correct relation is: \(1 \mathrm{~atm}=760 \mathrm{~mm} \mathrm{Hg}=76 \mathrm{~cm} \mathrm{Hg}\).

Step-by-step solution

Verify if the given relation is correct

To determine the correct conversion factors between atm, mmHg, and cmHg, let's recall the standard values: 1 atm = 760 mmHg. The given relation states that 1 atm = 760 cmHg. Since 10 mm = 1 cm, we need to convert 760 mmHg to cmHg.

Convert mmHg to cmHg

To convert 760 mmHg to cmHg, divide by 10: \[760 \mathrm{~mm} \mathrm{Hg} \cdot \frac{1 \mathrm{~cm}}{10 \mathrm{~mm}} = 76 \mathrm{~cm} \mathrm{Hg}\]

Correct the given relation

Based on the conversion, the correct relation should be: \[1 \mathrm{~atm} = 76 \mathrm{~mm} \mathrm{Hg} = 760 \mathrm{~mm} \mathrm{Hg}\] However, since we wanted to convert the units to cmHg, it should be: \[1 \mathrm{~atm} = 760 \mathrm{~mm} \mathrm{Hg} = 76 \mathrm{~cm} \mathrm{Hg}\] In conclusion, the given relation is false. The correct relation is: \(1 \mathrm{~atm}=760 \mathrm{~mm} \mathrm{Hg}=76 \mathrm{~cm} \mathrm{Hg}\).

Key concepts

Standard Atmosphere (atm)

Understanding atmospheric pressure is crucial in various scientific studies and practical applications, such as weather forecasting and aviation. The standard atmosphere (atm) is a unit of pressure defined as being precisely equal to 101,325 pascals or 101.325 kilopascals. It represents the pressure exerted by the weight of the air at sea level and at a temperature of 15 degrees Celsius.

Essentially, the atm is a reference value that allows for the comparison of different pressure levels. It is interesting to note that the value of 1 atm is closely approximate to the average atmospheric pressure at sea level on Earth. When we say that a tire is inflated to '2 atm,' we mean that the air inside is at a pressure two times that of the standard atmospheric pressure.

In the context of the original exercise, it's important to correct any misconceptions that may arise about the equivalent values of 1 atm in terms of mmHg or cmHg. This correction is fundamental as it helps avoid errors in calculations that involve pressure.

mmHg to cmHg Conversion

The units millimeters of mercury (mmHg) and centimeters of mercury (cmHg) are both measurements of pressure based on the height of a column of mercury in a barometer. Their names come from the early method of measuring atmospheric pressure using a column of mercury in a tube. One mmHg is the pressure exerted at the base of a 1-millimeter high column of mercury, and similarly, 1 cmHg is the pressure at the base of a 1-centimeter high column of mercury.

To convert from mmHg to cmHg, one needs to recognize the relationship between millimeters and centimeters. Since 1 cm equals 10 mm, we can convert mmHg to cmHg by dividing the number of mmHg by 10. For instance, if we have 760 mmHg and we want to convert it to cmHg, we simply divide 760 by 10, yielding 76 cmHg. This straightforward conversion is necessary for accurate measurements and reporting in scientific and medical contexts.

Pressure Unit Conversion

Pressure unit conversion is a fundamental skill in fields such as physics, engineering, and meteorology. Being adept at converting between different pressure units—such as atm, mmHg, cmHg, pascals (Pa), and others—is essential for accurate data interpretation and application.

Aside from the atm and mercury-related units, the pascal is the SI unit of pressure, defined as one newton per square meter. There are also other units like bars, where 1 bar is approximately equal to 0.98692 atm. Since pressure units are not interchangeable, proper conversion using established equivalence is critical. For instance, converting atm to pascals involves multiplying the atmospheric pressure by the conversion factor of 101,325.

To ensure precision in scientific calculations, it's imperative to not only understand how to perform these conversions but also to grasp the underlying principles that define each unit of pressure. Using correct conversion factors avoids errors and confusion, thus enhancing the accuracy of scientific communication and operations.