A steel-belted radial automobile tire is inflated to a gauge...

A steel-belted radial automobile tire is inflated to a gauge pressure of $30.0 \mathrm{lb} / \mathrm{in}^{2}$ when the temperature is $61^{\circ} \mathrm{F}$. Later in the day, the temperature rises to $100^{\circ} \mathrm{F}$ Assuming the volume of the tire remains constant, what is the tire's pressure at the elevated temperature? [Hint: Remember that the ideal gas law uses absolute pressure.]

A steel-belted radial automobile tire is inflated to a gauge pressure of $30.0 \mathrm{lb} / \mathrm{in}^{2}$ when the temperature is $61^{\circ} \mathrm{F}$. Later in the day, the temperature rises to $100^{\circ} \mathrm{F}$ Assuming the volume of the tire remains constant, what is the tire's pressure at the elevated temperature? [Hint:
Remember that the ideal gas law uses absolute pressure.]

Key Concepts

Ideal Gas Law

The Ideal Gas Law (PV = nRT) explains the relationship between pressure, volume, temperature, and the number of moles of gas. It is crucial in understanding how changes in temperature or volume can affect the pressure of a gas, assuming the amount of gas remains constant. In problems where one of these variables changes while others remain fixed, the law provides a direct proportional relationship that can be used to solve for the unknown variable.

Absolute Pressure vs Gauge Pressure

Absolute pressure is the total pressure exerted by a gas, including atmospheric pressure, whereas gauge pressure measures the pressure relative to the ambient atmospheric pressure. In many applications, like the analysis involving the Ideal Gas Law, it is important to use absolute pressure to accurately reflect the total energy within the system.

Temperature Conversion to Absolute Scale

Temperature must be expressed in an absolute scale (such as Kelvin or Rankine) when applying the Ideal Gas Law. This conversion ensures that proportional relationships between temperature and pressure are maintained correctly, since absolute zero is the point where the kinetic energy of the particles theoretically reaches zero.

Constant Volume Process

In a constant volume process, the volume of the system remains fixed while other variables like temperature and pressure may change. Under such circumstances, the Ideal Gas Law simplifies to a direct proportionality between pressure and temperature (when both are measured in absolute units), making it easier to calculate the new pressure after a temperature change.

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