A bicycle tire is inflated to a gauge pressure of 2.50 atm...

A bicycle tire is inflated to a gauge pressure of 2.50 atm when the temperature is $15.0^{\circ} \mathrm{C}$ . While a man rides the bicycle, the temperature of the tire rises to $45.0^{\circ} \mathrm{C}$ . Assuming the volume of the tire does not change, find the gauge pressure in the tire at the higher temperature.

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Key Concepts

Ideal Gas Law

The ideal gas law relates pressure, volume, temperature, and number of moles in a gas (PV = nRT). In scenarios where the volume remains constant, the pressure of a gas is directly proportional to its absolute temperature (in Kelvin). This concept allows for predicting how a change in temperature affects the gas pressure in a fixed-volume container.

Temperature Conversion

Since the ideal gas law requires the temperature to be in absolute units, it is necessary to convert Celsius temperatures to Kelvin. The conversion is done by adding 273.15 to the Celsius temperature. This step is crucial because using Kelvin ensures that the proportionality between pressure and temperature is applied correctly.

Gauge Pressure vs. Absolute Pressure

Gauge pressure measures the pressure relative to the ambient atmospheric pressure, while absolute pressure is the total pressure including atmospheric pressure. Since many gas law calculations use absolute pressure, understanding the relationship between gauge and absolute pressures is important, especially in practical problems involving pressurized systems like tires.

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