The total pressure in a \(11.7-\) Lautomobile tire is 44 psi at \(11^{\circ} \mathrm{C}\). How much does the pressure in the tire rise if its temperature increases to \(37{ }^{\circ} \mathrm{C}\) and the volume remains at \(11.7 \mathrm{~L}\) ?

Gas pressure calculation is a fundamental aspect of understanding gaseous behavior in various conditions, particularly when applying the Ideal Gas Law. The law itself is a cornerstone in chemistry and physics, encapsulating the relationship between pressure (P), volume (V), temperature (T), and the number of moles of gas (n). It is expressed as PV = nRT, where R is the universal gas constant.

For problems like our example with the automobile tire, knowing how to calculate gas pressure is crucial. Since the volume and the amount of gas do not change, we simplify the equation to a direct relationship between pressure and temperature. Hence, in this particular tire scenario, as the temperature rises, so does the air pressure, assuming the tire's volume remains fixed and no air is added or escapes. This simplified formula, P1/T1 = P2/T2, is what we use to calculate the new pressure after a temperature change.

Temperature conversion between the Celsius and Kelvin scales is an essential skill in scientific calculations, especially when dealing with gas laws. The Kelvin scale is used in these equations because it's an absolute temperature scale, meaning it starts from absolute zero, the point where particles theoretically stop moving.

The conversion is surprisingly straightforward: simply add 273.15 to the Celsius temperature to get Kelvin. In our tire example, we're given temperatures in Celsius, which are not directly applicable in the Ideal Gas Law. Therefore, we convert 11°C to 284.15K and 37°C to 310.15K to proceed with our calculations. Understanding how to properly convert temperatures can prevent calculation errors and misconceptions about the behavior of gases.

The Kelvin scale is critical for gas calculations because, unlike Celsius or Fahrenheit, it is an absolute scale. The significance of zero on the Kelvin scale, or absolute zero, is that it represents the point at which molecular motion ceases entirely - no thermal energy remains in the system. This positions the Kelvin scale as a true measure of the thermal energy within a substance.

One helpful tip to always keep in mind is that a temperature difference of one Kelvin is equivalent to one degree Celsius. This makes calculating temperature differences between two points on the Kelvin scale as easy as it is on the Celsius scale. It's also worth noting that in working with gases, the Kelvin scale ensures that all temperature values are positive, which is essential because you cannot have a negative amount of thermal energy.