You then breathe in and out again, and again, repeating this Boyle’s law cycle for the rest of your life ( Figure 9.15). When you exhale, the process reverses: Your diaphragm and rib muscles relax, your chest cavity contracts, and your lung volume decreases, causing the pressure to increase (Boyle’s law again), and air flows out of the lungs (from high pressure to low pressure). This causes air to flow into the lungs (from high pressure to low pressure). The increase in volume leads to a decrease in pressure (Boyle’s law). When you inhale, your diaphragm and intercostal muscles (the muscles between your ribs) contract, expanding your chest cavity and making your lung volume larger.
Lungs are made of spongy, stretchy tissue that expands and contracts while you breathe. Your lungs take in gas that your body needs (oxygen) and get rid of waste gas (carbon dioxide). How does it work? It turns out that the gas laws apply here. What do you do about 20 times per minute for your whole life, without break, and often without even being aware of it? The answer, of course, is respiration, or breathing. Taking P 1 and T 1 as the initial values, T 2 as the temperature where the pressure is unknown and P 2 as the unknown pressure, and converting ☌ to K, we have: (b) We are looking for a pressure change due to a temperature change at constant volume, so we will use Amontons’s/Gay-Lussac’s law. (Also, isobutane is combustible, so incineration could cause the can to explode.) High temperature could lead to high pressure, causing the can to burst. (a) The can contains an amount of isobutane gas at a constant volume, so if the temperature is increased by heating, the pressure will increase proportionately. If the can is left in a car that reaches 50 ☌ on a hot day, what is the new pressure in the can? (b) The gas in the can is initially at 24 ☌ and 360 kPa, and the can has a volume of 350 mL. (a) On the can is the warning “Store only at temperatures below 120 ☏ (48.8 ☌). Predicting Change in Pressure with TemperatureĪ can of hair spray is used until it is empty except for the propellant, isobutane gas. (Also note that there are at least three ways we can describe how the pressure of a gas changes as its temperature changes: We can use a table of values, a graph, or a mathematical equation.) Note that temperatures must be on the kelvin scale for any gas law calculations (0 on the kelvin scale and the lowest possible temperature is called absolute zero). This equation is useful for pressure-temperature calculations for a confined gas at constant volume. If the gas is initially in “Condition 1” (with P = P 1 and T = T 1), and then changes to “Condition 2” (with P = P 2 and T = T 2), we have that P 1 T 1 = k P 1 T 1 = k and P 2 T 2 = k, P 2 T 2 = k, which reduces to P 1 T 1 = P 2 T 2.
Where ∝ means “is proportional to,” and k is a proportionality constant that depends on the identity, amount, and volume of the gas.įor a confined, constant volume of gas, the ratio P T P T is therefore constant (i.e., P T = k P T = k).
P ∝ T or P = constant × T or P = k × T P ∝ T or P = constant × T or P = k × T
We will consider the key developments in individual relationships (for pedagogical reasons not quite in historical order), then put them together in the ideal gas law. Eventually, these individual laws were combined into a single equation-the ideal gas law-that relates gas quantities for gases and is quite accurate for low pressures and moderate temperatures. Although their measurements were not precise by today’s standards, they were able to determine the mathematical relationships between pairs of these variables (e.g., pressure and temperature, pressure and volume) that hold for an ideal gas-a hypothetical construct that real gases approximate under certain conditions.