An automobile tire is inflated with air originally at 10.0^∘ C and normal atmospheric pressure.

step 1 Okay, I've just written down the given quantities and we just want to solve for P2 in this tire.

An automobile tire is inflated with air originally at 10.0^∘...

An automobile tire is inflated with air originally at $10.0^{\circ} \mathrm{C}$ and normal atmospheric pressure. During the process, the air is compressed to 28.0$\%$ of its original volume and the temperature is increased to $40.0^{\circ} \mathrm{C} .$ (a) What is the tire pressure? (b) After the car is driven at high speed, the tire's air temperature rises to $85.0^{\circ} \mathrm{C}$ and the tire's interior volume increases by 2.00$\%$ . What is the new tire pressure (absolute)?

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Key Concepts

Ideal Gas Law

The ideal gas law (PV = nRT) is central to relating pressure, volume, and temperature for gases. It allows us to calculate changes in one variable when the others are altered, making it essential for problems that involve compression or heating of a gas.

Temperature Conversion to Kelvin

Converting temperatures from Celsius to Kelvin is crucial when using the ideal gas law because the law requires absolute temperature scales. This conversion ensures accurate calculations and proper proportionality in gas law equations.

Volume and Pressure Relationships

Understanding how volume and pressure interact is key; for a constant amount of gas at a given temperature, a reduction in volume leads to an increase in pressure and vice versa. This principle, embodied in Boyle’s Law, forms part of the broader ideal gas behavior.

Handling Non-Isothermal Process Changes

When a gas undergoes both changes in volume and temperature, it is important to account for both effects simultaneously using the ideal gas law. This involves adjusting calculations to reflect the combined influence of compression and temperature rise or drop on the pressure.

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