diff --git a/content/physics/thermodynamics.md b/content/physics/thermodynamics.md index b97e523..3a87ffd 100644 --- a/content/physics/thermodynamics.md +++ b/content/physics/thermodynamics.md @@ -114,3 +114,88 @@ b=\frac{L}{4\pi r^2} $$ The above is true when $L$ is procured from the source, most likely using the Boltzmann's law. +# Gas Laws and the Ideal Gas Law + +## Ideal Gas Law +The **Ideal Gas Law** is a fundamental equation describing the behavior of ideal gases: + +$$ +PV = nRT +$$ + +Where: +- $P$ = Pressure (in atm, Pa, or another unit) +- $V$ = Volume (in liters or cubic meters) +- $n$ = Number of moles of gas +- $R$ = Ideal gas constant ($0.0821 \, \mathrm{L \cdot atm \cdot mol^{-1} \cdot K^{-1}}$) +- $T$ = Temperature (in Kelvin) + +This equation relates the pressure, volume, temperature, and quantity of an ideal gas. + +--- + +## Boyle's Law +**Boyle's Law** states that the pressure of a gas is inversely proportional to its volume when temperature and the number of moles are constant: + +$$ +P \propto \frac{1}{V} \quad \text{or} \quad P_1V_1 = P_2V_2 +$$ + +### Key Points: +- As volume decreases, pressure increases. +- The relationship is hyperbolic. + +--- + +## Charles's Law +**Charles's Law** states that the volume of a gas is directly proportional to its absolute temperature when pressure and the number of moles are constant: + +$$ +V \propto T \quad \text{or} \quad \frac{V_1}{T_1} = \frac{V_2}{T_2} +$$ + +### Key Points: +- As temperature increases, volume increases. +- Temperature must be in Kelvin. + +--- + +## Gay-Lussac's Law +**Gay-Lussac's Law** states that the pressure of a gas is directly proportional to its absolute temperature when volume and the number of moles are constant: + +$$ +P \propto T \quad \text{or} \quad \frac{P_1}{T_1} = \frac{P_2}{T_2} +$$ + +### Key Points: +- As temperature increases, pressure increases. +- Temperature must be in Kelvin. + +--- + +## Avogadro's Law +**Avogadro's Law** states that the volume of a gas is directly proportional to the number of moles when pressure and temperature are constant: + +$$ +V \propto n \quad \text{or} \quad \frac{V_1}{n_1} = \frac{V_2}{n_2} +$$ + +### Key Points: +- Adding more gas increases volume proportionally. +- This law explains why equal volumes of gases contain equal numbers of molecules at the same temperature and pressure. + +--- + +## Combined Gas Law +The **Combined Gas Law** combines Boyle's, Charles's, and Gay-Lussac's Laws into one equation when the number of moles is constant: + +$$ +\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2} +$$ + +This equation can be used to calculate changes in pressure, volume, or temperature of a gas sample. + +--- + +Use these laws to analyze relationships between variables and predict gas behavior under different conditions! +