A tire on a car is inflated to a gauge pressure of 32 lb / in^2 at a temperature of 27^∘ C. Afte

step 1 So in this question, we have a tire of on a car having initial gauge pressure P initial gauge eq

A tire on a car is inflated to a gauge pressure of 32 lb /...

A tire on a car is inflated to a gauge pressure of $32 \mathrm{lb} / \mathrm{in}^{2}$ at a temperature of $27^{\circ} \mathrm{C}$. After the car is driven for $30 \mathrm{mi}$, the pressure has increased to $34 \mathrm{lb} / \mathrm{in}^{2}$. What is the temperature of the air inside the tire at this point? a) $40 .{ }^{\circ} \mathrm{C}$ b) $23^{\circ} \mathrm{C}$ c) $32^{\circ} \mathrm{C}$ d) $54^{\circ} \mathrm{C}$

A tire on a car is inflated to a gauge pressure of $32 \mathrm{lb} / \mathrm{in}^{2}$ at a temperature of $27^{\circ} \mathrm{C}$. After the car is driven for $30 \mathrm{mi}$, the pressure has increased to $34 \mathrm{lb} / \mathrm{in}^{2}$. What is the temperature of the air inside the tire at this point?
a) $40 .{ }^{\circ} \mathrm{C}$
b) $23^{\circ} \mathrm{C}$
c) $32^{\circ} \mathrm{C}$
d) $54^{\circ} \mathrm{C}$

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Key Concepts

Constant Volume Process

In a constant volume process, such as the air inside a tire, the volume remains fixed. This characteristic implies that any change in the pressure of the gas is solely due to changes in temperature (assuming the number of moles of gas remains constant), as laid out by the ideal gas law.

Temperature Conversion

Temperature for the ideal gas law must be expressed in Kelvin rather than Celsius. Converting from Celsius to Kelvin by adding 273.15 ensures that the relationship between pressure and temperature is used correctly in the calculations.

Ideal Gas Law

The ideal gas law (PV=nRT) establishes a direct relationship between pressure and temperature for an ideal gas when the volume and amount of gas remain constant. In this context, because the tire's volume does not change, any increase in pressure is directly proportional to the increase in the absolute temperature measured in Kelvin.

Gauge Pressure vs. Absolute Pressure

Gauge pressure is the pressure measured relative to ambient atmospheric pressure, whereas absolute pressure includes the atmospheric component. For accurate calculations using the ideal gas law, it is essential to convert gauge pressure to absolute pressure by adding the atmospheric pressure value.

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