Show how Boyle‘s law and Charles‘s law are special cases of the ideal gas law.
Interpretation:
How the Boyle’s law and Charle’s law are special cases of the ideal gas law should be explained.
Concept introduction:
An ideal gas can be categorized by three variables state: absolute pressure (P), absolute temperature (T) and volume (V), and the relationship between them are expressed in terms of ideal gas law.
Ideal gas law is a hypothetical law and is mathematically expressed as:
PV = nRT
Where,
P is the pressure of gas
V is the volume of the gas
T is the absolute temperature of the gas
R is the gas constant and
n is the number of moles of the gas molecules
Boyle’s law determines the relation between pressure and volume at a constant temperature for a fixed amount of gas. Boyle’s law is expressed as:
That is pressure is inversely proportional to the volume for a fixed amount of gas at a particular temperature.
Charle’s law determines the relation between volume and the temperature (kelvin) for a fixed amount of gas when the pressure is held constant. The law is expressed as:
That is volume is directly proportional to the temperature (kelvin) for a fixed amount of gas when at a particular pressure.
Both Boyle’s law and Charle’s law are special case of ideal gas law and can be derived from the ideal gas law as follows:
The ideal gas laws
PV = nRT
Now when T and n is constant, the ideal gas equation become
PV = Constant
Similarly, when P and n is constant, the ideal gas equati
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