The gage pressure of an automobile tire is measured to be 200 kPa before a trip and 220 kPa afte

step 1 P1 is atmospheric pressure plus gauge pressure equals 290 pascal and P2 is the atmospheric press

The gage pressure of an automobile tire is measured to be...

The gage pressure of an automobile tire is measured to be $200 \mathrm{kPa}$ before a trip and $220 \mathrm{kPa}$ after the trip at a location where the atmospheric pressure is 90 kPa. Assuming the volume of the tire remains constant at $0.035 \mathrm{m}^{3},$ determine the percent increase in the absolute temperature of the air in the tire.

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Key Concepts

Ideal Gas Law

The ideal gas law, expressed as PV = nRT, relates the pressure (P), volume (V), temperature (T), and amount (n) of an ideal gas. In situations where the volume remains constant, as in the case with a rigid tire, the pressure is directly proportional to the absolute temperature. This principle allows one to determine changes in temperature from the corresponding changes in pressure.

Constant Volume Process

A constant volume process implies that the volume of the gas does not change during the process, so any variation in pressure must be due to changes in temperature (assuming the number of moles remains constant). This concept is crucial when applying the direct proportionality between absolute pressure and temperature to analyze how temperature varies with pressure.

Gauge Pressure and Absolute Pressure

Gauge pressure is the pressure measured relative to the ambient atmospheric pressure, while absolute pressure includes the atmospheric pressure. In thermodynamic problems, especially those involving the ideal gas law, it is necessary to use the absolute pressure in calculations. Converting gauge pressure to absolute pressure by adding atmospheric pressure is a key step in relating pressure to temperature.

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