An automobile tire has a volume of 0.0150 m^3 on a cold day when the temperature of the air in t

step 1 Hello, so in this problem we want to find the pressure inside an automobile time after it has mo

An automobile tire has a volume of 0.0150 m^3 on a cold day...

An automobile tire has a volume of 0.0150 $\mathrm{m}^{3}$ on a cold day when the temperature of the air in the tire is $5.0^{\circ} \mathrm{C}$ and atmospheric pressure is 1.02 atm. Under these conditions the gauge pressure is measured to be 1.70 atm (about 25 $\mathrm{lb} / \mathrm{in.} .$ ). After the car is driven on the highway for 30 min, the temperature of the air in the tires has risen to $45.0^{\circ} \mathrm{C}$ and the volume has risen to 0.0159 $\mathrm{m}^{3}$ . What then is the gauge pressure?

Key Concepts

Gauge Pressure vs. Absolute Pressure

Understanding the difference between gauge pressure and absolute pressure is important in contexts where measured pressures are given relative to atmospheric pressure. Absolute pressure is the total pressure exerted by the gas including atmospheric pressure, whereas gauge pressure is the pressure measured above or below the ambient atmospheric pressure.

Combined Gas Law

The combined gas law is derived from the ideal gas law by considering a constant amount of gas and relates the pressure, volume, and temperature between two states through the equation (P1V1/T1 = P2V2/T2). This concept is instrumental when analyzing scenarios where multiple state variables change simultaneously, allowing one to solve for unknown parameters such as final pressure after temperature and volume modifications.

Temperature Conversion

Temperature conversion, particularly from Celsius to Kelvin, is essential when applying the ideal gas law since the Kelvin scale is the absolute temperature scale required in gas law calculations. This conversion is done by adding 273.15 to the Celsius temperature, ensuring that the calculation of gas behavior is accurate.

Ideal Gas Law

The ideal gas law (PV = nRT) is a fundamental equation in thermodynamics that describes the relationship among the pressure (P), volume (V), temperature (T), and amount of gas (n) under the ideal assumption that the gas particles do not interact. This law is crucial in understanding how changes in temperature and volume affect the pressure of a gas, assuming the number of moles remains constant.

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