Utotal of Ideal Gas

[Janice Xiao 1I]

What is the significance of the 3/2 in Utotal=3/2*nRT?

[Shannon Wasley 2J]

The molar heat capacity for a monatomic gas at constant volume, C (v,m) is 3/2R. Therefore when we use the equation q = nC(m)deltaT, we get q = n 3/2RdeltaT, when we plug in our molar heat capacity for a monatomic gas. Since this molar heat capacity is at constant volume, delta V = 0 and therefore w = 0. So delta U is equal to n 3/2RdeltaT. The value of the molar heat capacity changes based on whether it is for constant volume or constant pressure and if it is atoms, linear or nonlinear molecules. These values can be found on page 281 in the book.

[Danah Albaaj 1I]

It has to do with the kinetic energy of the ideal gas. I recommend reading section 8.7 where it goes into great detail on how the numbers come into play through the use of Boltzmann's constant and the Ideal Gas Law alongside the equipartition theorem. Professor Lavelle also briefly went over it while deriving the equation for reversible, isothermal expansion work during lecture 7.

[Guadalupe T 1E]

When you have constant volume and you have to use the equation: change in S=nRln(v2/v1) the R(8.314) has to be multiplied by 3/2.