PUMPA - SMART LEARNING

எங்கள் ஆசிரியர்களுடன் 1-ஆன்-1 ஆலோசனை நேரத்தைப் பெறுங்கள். டாப்பர் ஆவதற்கு நாங்கள் பயிற்சி அளிப்போம்

Book Free Demo
Derive the ideal gas equation.
 
Benoît Paul Émile Clapeyron first proposed the ideal gas equation in  as a combination of Boyle's law, Charles's law and Avogadro's law.
 
The ideal gas equation is an equation, which relates all the properties of an ideal gas.

An ideal gas  Boyle’s law and Charles’ law and Avogadro’s law.
  
According to Boyle’s law,
 
iαiiatconstantnandi ----- (Eq. 1)
 
According to Charles’s law,

iαiatconstantnandi ----- (Eq. 2)
According to Avogadro’s law,
 
iαiatconstantiandi ----- (Eq. 3)
 
Combining equations (Eq. 1), (Eq. 2) and (Eq. 3),
 
Rearranging the equation,
 ----- (Eq. 4)
 
The above relation is called the combined law of gases.
 
Consider a gas, which contains μ moles of the gas, the number of atoms contained will be equal to,
 ----- (Eq. 5)
 
Substitute the Eq. 5 to Eq. 4, then the Eq. 4 can be written as,
 ----- (Eq. 6)
 
The value of the constant in the above equation is taken to be KB, which is called as Boltzmann constant (1.38×1023JK1).
 
Hence, we have the following equation:
 ----- (Eq. 6)
 
Here,
,
 
which is termed as universal gas constant whose value is 8.31Jmol1K1.
 
Substitute the value of \(R\) in the equation,
 
 
Ideal gas equation is also called as equation of state because it gives the relation between the state variables and it is used to describe the state of any gas.