The combined gas law is a gas law which combines Charles's law, Boyle's law, and Gay-Lussac's law. The combined gas law integrates Charles’s law, Boyle’s law, and Gay-Lussac’s law. Each of these gas laws relates one thermodynamic variable to another mathematically, but holds everything else constant. Each of the combined laws shows that two variables are in proportion to one another, while the combined gas law itself demonstrates that these three laws are actually inter-dependent.
Gas Equation: P_{i}V_{i}/T_{i} = P_{f}V_{f}/T_{f}
where,
V_{i} = Initial Volume,
P_{i} = Initial Pressure,
T_{i} = Initial Temperature,
V_{f} = Final Volume,
P_{f} = Final Pressure,
T_{f} = Final Temperature.
These laws each relate one thermodynamic variable to another mathematically while holding everything else constant. Charles's law states that volume and temperature are directly proportional to each other as long as pressure is held constant. Boyle's law asserts that pressure and volume are inversely proportional to each other at fixed temperature. Finally, Gay-Lussac's law introduces a direct proportionality between temperature and pressure as long as it is at a constant volume. The inter-dependence of these variables is shown in the combined gas law, which clearly states that: The ratio between the pressure-volume product and the temperature of a system remains constant.
Example:
Calculate the Final temperature by using the Combined Law.
Initial Volume (Vi) = 25 L
Initial Pressure (Pi) = 10 kPa
Initial Temperature (Ti) = 5 K
Final Volume (Vf) = 15 L
Final Pressure (Pf) = 20 kPa
Solution:
Apply Formula:
Gas Equation: P_{i}V_{i}/T_{i} = P_{f}V_{f}/T_{f
}Final Temperature (Tf) = 6 K