You fill your car tires with air on a cold morning (0^∘ C) to a gauge pressure of 210 kPa. As yo

step 1 this will be given the initial temperature is equal to 0 degree centigrade which is equal to 273

You fill your car tires with air on a cold morning (0^∘ C)...

You fill your car tires with air on a cold morning $\left(0^{\circ} \mathrm{C}\right)$ to a gauge pressure of $210 \mathrm{kPa}$. As you drive, friction and the warming day increase the air temperature inside the tire to $45^{\circ} \mathrm{C},$ while the volume remains constant. What's the new gauge pressure? (a) 210 $\mathrm{kPa}$; (b) $233 \mathrm{kPa}$; (c) $244 \mathrm{kPa}$ (d) $261 \mathrm{kPa}$.

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Key Concepts

Ideal Gas Law

The ideal gas law relates the pressure, volume, temperature, and amount of a gas through the equation PV = nRT. This principle helps us understand how changes in temperature, while holding volume constant, directly affect the pressure of a gas.

Constant Volume Process

In a constant volume process, the volume of the gas does not change. This means that any change in temperature will solely result in a proportional change in pressure, as described by the ideal gas law, making the ratio of pressure to temperature constant.

Temperature Conversion

Temperature must be expressed in an absolute scale—usually Kelvin—when using the ideal gas law. Converting from Celsius to Kelvin (by adding 273) ensures that the thermodynamic calculations are accurate and physically meaningful.

Gauge Pressure vs Absolute Pressure

Gauge pressure is measured relative to atmospheric pressure, while absolute pressure includes the atmospheric pressure. When applying gas laws, it is important to use absolute pressures, and then convert back to gauge pressure by subtracting the atmospheric pressure if needed.

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