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Change of state of an ideal gas according to Charles's law
Equation
Charles's Law states that with the pressure ($p$) held constant, the following relationship exists between the absolute temperature ($T$) and the volume ($V$):
This means that if a gas transitions from an initial state (i) to a final state (f) with the pressure ($p$) and the number of particles ($N$) held constant, it occurs in such a way that with the volume in state i ($V_i$), the volume in state f ($V_f$), the temperature in initial state ($T_i$), and the temperature in final state ($T_f$):
 $\displaystyle\frac{ V_i }{ T_i }=\displaystyle\frac{ V_f }{ T_f }$ |
ID:(3492, 0)
Change of state of an ideal gas according to the Gay Lussac Law
Equation
The Gay-Lussac's Law states that with the volume ($V$) held constant, the following relationship between the absolute temperature ($T$) and the pressure ($p$) holds:
This means that if a gas transitions from an initial state (i) to a final state (f) with the pressure ($p$) and the number of particles ($N$) held constant, it occurs in such a way that with the pressure in initial state ($p_i$), the pressure in final state ($p_f$), the temperature in initial state ($T_i$), and the temperature in final state ($T_f$), the following holds:
| $\displaystyle\frac{ p_i }{ T_i }=\displaystyle\frac{ p_f }{ T_f }$ |
ID:(3490, 0)
Change of state of an ideal gas according to Boyle's law
Equation
Boyle's Law states that with constant the absolute temperature ($T$), the following relationship holds for the pressure ($p$) and the volume ($V$):
This means that if a gas undergoes a change from an initial state (i) to a final state (f) with constant the absolute temperature ($T$) such that for the pressure in initial state ($p_i$), the pressure in final state ($p_f$), the volume in state i ($V_i$), and the volume in state f ($V_f$), the following relationship is satisfied:
| $ p_i V_i = p_f V_f $ |
ID:(3491, 0)
General Gas Law
Equation
In 1834, Émile Clapeyron recognized that the pressure ($p$), the volume ($V$), the absolute temperature ($T$), and the number of moles ($n$) are related by Boyle's law, Charles's law, Gay-Lussac's law, and Avogadro's law. These laws can be rewritten in the form:
| $ p V = n R T $ |
The pressure ($p$), the volume ($V$), the absolute temperature ($T$), and the number of moles ($n$) are related through the following physical laws:
• Boyle's law
| $ p V = C_{pV} $ |
• Charles's law
| $\displaystyle\frac{ V }{ T } = C_{VT}$ |
• Gay-Lussac's law
| $\displaystyle\frac{ p }{ T } = C_{pT}$ |
• Avogadro's law
| $\displaystyle\frac{ n }{ V } = C_{nV} $ |
These laws can be expressed in a more general form as:
$\displaystyle\frac{pV}{nT}=cte$
This general relationship states that the product of pressure and volume divided by the number of moles and temperature remains constant:
| $ p V = n R T $ |
In this equation, the universal gas constant ($R$) assumes the value 8.314 J/K·mol.
ID:(3183, 0)
Pressure as a function of molar concentration
Equation
When the pressure ($p$) behaves as an ideal gas, satisfying the volume ($V$), the number of moles ($n$), the absolute temperature ($T$), and the universal gas constant ($R$), the ideal gas equation:
| $ p V = n R T $ |
can be rewritten in terms of the molar concentration ($c_m$) as:
| $ p = c_m R T $ |
When the pressure ($p$) behaves as an ideal gas, satisfying the volume ($V$), the number of moles ($n$), the absolute temperature ($T$), and the universal gas constant ($R$), the ideal gas equation:
| $ p V = n R T $ |
and the definition of the molar concentration ($c_m$):
| $ c_m \equiv\displaystyle\frac{ n }{ V }$ |
lead to the following relationship:
| $ p = c_m R T $ |
ID:(4479, 0)