An automobile tire has a maximum rating of 38.0 psi (gauge pressure). The tire is inflated (while cold) to a volume of 11.8 L and a gauge pressure of 36.0 psi at a temperature of 12.0 C. When the car is driven on a hot day, the tire warms to 65.0 C and its volume expands to 12.2 L. Does the pressure in the tire exceed its maximum rating? (Note: The gauge pressure is the difference between the total pressure and atmospheric pressure. In this case, assume that atmospheric pressure is 14.7 psi.)

Understanding gauge pressure is critical when dealing with various practical applications such as checking the air in automobile tires. Gauge pressure is the pressure read on a gauge and represents the pressure difference between the interior of an object, like a tire, and the surrounding atmosphere. It's essentially the excess pressure over the atmospheric pressure.

Namely, gauge pressure does not include atmospheric pressure in its reading, which roughly equates to 14.7 psi at sea level. To get the absolute pressure, one must add the atmospheric pressure to the gauge pressure. This is a key concept when using the ideal gas law to calculate how the pressure inside a tire might change with temperature and volume fluctuations.

Temperatures in ideal gas law calculations must be expressed in Kelvin because it is an absolute temperature scale that begins at absolute zero, where all molecular motion theoretically stops. To convert Celsius to Kelvin, add 273.15 to the Celsius temperature.

This step is crucial for precision in gas law calculations. When working with the ideal gas law, consistency in units is key, and Kelvin provides a consistent standard because, unlike Celsius or Fahrenheit, it doesn't deal with negative numbers or vary according to the context such as weather or body temperature.

Absolute pressure is the total pressure exerted by a gas, and it includes atmospheric pressure. In other words, it's the sum of the gauge pressure and atmospheric pressure. It's a significant concept because when scientists or engineers speak about a 'vacuum,' they usually refer to a space with no absolute pressure.

In problems like the one about tire pressure, failing to account for absolute pressure can lead to incorrect conclusions. Knowing the absolute pressure is essential to understand precisely how close the pressure in a tire (or any closed system) is to its maximum tolerable limit, as it's the absolute pressure that determines the stress on the container's walls.

The ideal gas law, expressed as PV = nRT, is a cornerstone of studying gases and their behaviors. It allows for calculations of pressure (P), volume (V), temperature (T), and the amount of substance in moles (n), with R being the ideal gas constant.

When using the ideal gas law, assuming the amount of gas and the gas constant remains unchanged provides a way to understand how the other factors — volume, temperature, and pressure — influence each other. Gas law calculations allow for predicting the behavior of tire pressure in changing conditions, like when the temperature increases on a hot day. By setting up a proportionality based on initial conditions, one can calculate how temperature or volume changes will affect the pressure within a system without explicitly calculating the amount of gas or the constant.