The internal pressure on a bottle of soda is 5570 torr. The bottle cap is designed to withstand a pressure of \(7.0 \mathrm{~atm}\). (a) Calculate the pressure in atm. (b) Calculate the pressure in psi. (c) Calculate the pressure in \(\mathrm{kPa}\). (d) Is the bottle cap at risk of failing?

Understanding the conversion from torr to atmosphere (atm) units is essential in various sciences, particularly when dealing with the measurement of pressure.
One standard atmosphere is equivalent to 760 torr, which is a key conversion factor derived from the definition of 1 atm as the pressure exerted by a 760 mm column of mercury at 0 °C.

• To convert torr to atm, you divide the pressure value in torr by 760.

This process is crucial, for example, when a soda bottle's internal pressure is measured in torr but needs to be compared with the pressure tolerance given in atm. In the given exercise, a pressure of 5570 torr is converted into atm by dividing by 760, resulting in approximately 7.33 atm, which is a straightforward application of this important conversion.

The conversion between atmospheres (atm) and pounds per square inch (psi) is common in various engineering and physics applications.
To switch from atm to psi, the recognized conversion factor is 1 atm = 14.696 psi.

• The calculation involves multiplying the atmospheric pressure by 14.696 to obtain the pressure in psi.

The ease of this conversion simplifies comparative analyses between different pressure units in diverse settings – for instance, technicians using psi to gauge tyre pressure can relate this to atmospheric pressure measurements commonly used in weather reports.

The kilopascal (kPa) is a unit of pressure in the metric system and a subset of the International System of Units (SI). It is widely used in science and engineering to express smaller pressures where using pascals would result in large numbers.

• One atmosphere (1 atm) is equivalent to 101.325 kilopascals (kPa).

The conversion from atm to kPa, therefore, involves multiplying by 101.325.
Understanding kPa is crucial for interpreting readings from instruments such as barometers and for complying with the metric system's use in scientific research internationally.

Pressure is a fundamental concept in physics, defined as the force applied perpendicular to the surface of an object per unit area over which that force is distributed. It is a critical factor in the study of fluids, weather patterns, and in engineering designs like pressure vessels.

• Common units of pressure include torr, atmosphere (atm), pounds per square inch (psi), and kilopascals (kPa).
• Each unit has a specific area of application and usage depending on industry standards or regional preferences.

Comprehending these various units and their conversions is not only practical but imperative for accurately gauging pressures and ensuring the safety of pressure-sensitive systems like the soda bottle cap in our example.