What does translational energy have to do with entropy change?

[giggidygigg]

I know that the translational energy of gas can be represented by
3/2NkT
where N = number of molecules, k = boltzmann's constant, T = temperature

my textbook says that the change in entropy is
(delta)S = (integral from 1 to 2) dS = (integral from 1 to 2) dU/T + (integral from 1 to 2) PdV/T = NRln(v2/v1)

i know that since U = 0 in an isothermal system, dU/T term gets canceled and the PdV/T term is left, but i don't understand how we get NRln(v2/v1) from it

i also don't know how translational energy comes into place.

much help needed!

 

[mdelisio]

Try using the ideal gas law PV = NRT to put the P/T in terms of V. Hope this helps.

 

[astrokreng]

Translational energy and entropy change are closely related in the context of thermodynamics. To understand this, let's first define translational energy and entropy.

Translational energy refers to the kinetic energy of molecules in a gas, which is directly related to their velocity and mass. In other words, it is the energy associated with the random motion of gas molecules.

Entropy, on the other hand, is a measure of the disorder or randomness in a system. It is a thermodynamic property that describes the number of possible arrangements or microstates that a system can have.

Now, let's consider the ideal gas law, which states that the product of pressure and volume is directly proportional to the number of molecules (N), temperature (T), and Boltzmann's constant (k). In other words, PV = NkT.

Using this equation, we can express the change in entropy (ΔS) as ΔS = Nk ln(V2/V1), where V2 and V1 are the final and initial volumes, respectively. This equation is derived from the fact that the entropy of an ideal gas is directly proportional to the natural logarithm of its volume.

So, how does translational energy come into play? As mentioned earlier, translational energy is directly related to the velocity and mass of gas molecules. When the temperature of a gas increases, the translational energy of its molecules also increases. This means that the molecules will have higher velocities and will occupy a larger volume, leading to an increase in entropy.

In summary, the change in entropy is directly related to the change in volume, which is in turn related to the translational energy of gas molecules. This is why the ideal gas law and the expression for entropy change both involve the number of molecules and temperature.