- slide 1 of 7
The Ideal Gas Law and Avogadro's Number
In terms of Avogadro's number NA, we can write the number of moles n as:
1) n = N/NA
where N represents the total number of molecules in a gas and NA = 6.02 x 1023 molecules/mole. We found in part one that the ideal gas law may be written as:
2) PV = nRT
Substituting 1 into 2 yields:
3) PV = N/NART
We can simplify this equation even further with the use of Boltzmann's contant. Boltzmann's constant is defined as:
4) k = R/NA
which is 1.38 x 10-23 J/K in SI units. Then equation 3 becomes:
5) PV = NkT
This is another standard way of writing the ideal gas equation.
- slide 2 of 7
6) P1V1 / T1 = P2V2 / T2
where P1,V1, and T1 are the original values of the gas, while P2,V2, and T2 represent its final values.
We can use equation 6 to derive Boyle's, Charles', and Gay-Lussac's Laws. We do this by considering isothermal, isobaric, and isochoric thermodynamic processes.
- slide 3 of 7
Derivation of Boyle's Law
Isothermal means that the temperature is constant. When we do this, T1 = T2 = T, so:
7) P1V1 / T = P2V2 / T
The Ts cancel, and we are left with Boyle's Law P1V1 = P2V2.
- slide 4 of 7
Derivation of Charles' Law
Isobaric means that the pressure is constant, so P1 = P2 = P, giving us:
8) PV1 / T1 = PV2 / T2
With the Ps canceling, we are left with Charles' Law V1/T1 = V2/T2.
- slide 5 of 7
Derivation of Gay-Lussac's Law
Finally, isochoric means the volume is constant, such that V1 = V2 = V, and thus we have:
9) P1V / T1 = P2V / T2
The Vs cancel, giving us Gay-Lussac's Law P1/T1 = P2/T2.
- slide 6 of 7
Physics for Scientists and Engineers by Douglas Giancoli
Fundamentals of Physics by Halliday, Resnick, and Walker
Ideal gas law from www.EngineersEdge.com
- slide 7 of 7
Other Forms of the Ideal Gas Law
This series gives an elementary, non-calculus based introduction to the ideal gas law, including an account of its origins and how to use it to derive Boyle's, Charles', and Gay-Lussac's Laws.