A bicycle tire has a pressure of 7.00 ×10^5 N / m^2 at a temperature of 18.0^∘ C and contains 2.

step 1 So we have a tire with a pressure of 7 .00 into 10 par 5 Newton per meter square. Remember that

A bicycle tire has a pressure of 7.00 ×10^5 N / m^2 at a...

A bicycle tire has a pressure of $7.00 \times 10^{5} \mathrm{N} / \mathrm{m}^{2}$ at a temperature of $18.0^{\circ} \mathrm{C}$ and contains $2.00 \mathrm{L}$ of gas. What will its pressure be if you let out an amount of air that has a volume of $100 \mathrm{cm}^{3}$ at atmospheric pressure? Assume tire temperature and volume remain constant.

Key Concepts

Direct Proportionality of Pressure to Number of Moles

When a system undergoes an isothermal process in a fixed volume, the pressure of the gas is directly proportional to the number of moles present. This means that if some gas is removed from the system, the pressure decreases proportionally. This concept, derived from the Ideal Gas Law, is key to solving problems involving the removal or addition of gas at constant temperature and volume.

Isothermal Process

An isothermal process is one in which the temperature remains constant throughout. In such a process, if the volume is also fixed, any change in the number of moles directly alters the pressure. This principle is crucial for understanding how releasing gas from the system will lower the internal pressure.

Mole Concept

The mole concept is essential for converting between a given volume of gas (at specific pressure and temperature) and the number of moles it contains. This concept allows one to quantitatively analyze how changes in the amount of gas influence the system, particularly when using the Ideal Gas Law to relate these changes to pressure.

Ideal Gas Law

The Ideal Gas Law (PV = nRT) establishes the relationship between pressure, volume, number of moles, and temperature for a gas. This law is fundamental in determining how variations in one or more of these state variables affect the others, and it is key to problems where a gas is added or removed under controlled conditions.

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