Calculating Entropy Change in a Diatomic Gas Sample

[SwMarc]

My prof gave us a question to take home and examine and review because he had to leave on urgent family matters so as a result we had to teach a chapter to ourselves about thermodynamics. Inside the chapter is a section on Entropy which I am getting really hung up on, but anyways here is the question...

The initial state of a diatomic gas sample is given by P1, V1, n1, and T1.
The gas sample expands from volume V1 to Volume 2V1.
Calculate the entropy change of the gas in terms of the above initial variables and the gas constant R if:
a. The expansion takes place at constant presssure
b. The expansion is Isothermal
c. The expansion is adiabatic
d. The expansion takes place in a repitition of joules free expansion experiment.

I sort of have a but its only halfass so I guess I need help/pointers on any of the parts.
Thanks!

 

[Astronuc]

What formula or relationship are you using?

 

[Andrew Mason]

My prof gave us a question to take home and examine and review because he had to leave on urgent family matters so as a result we had to teach a chapter to ourselves about thermodynamics. Inside the chapter is a section on Entropy which I am getting really hung up on, but anyways here is the question...

The initial state of a diatomic gas sample is given by P1, V1, n1, and T1.
The gas sample expands from volume V1 to Volume 2V1.
Calculate the entropy change of the gas in terms of the above initial variables and the gas constant R if:
a. The expansion takes place at constant presssure

From the relationship P = nRT/V you can see that if P is constant and V increases, T must increase in proportion to V. So the final T = 2T1. Heat must obviously be transferred to the gas.

Entropy change is the heat transfer divided by temperature: dS = dQ/T
From the first law, keeping in mind that P is constant:
$dQ = dU + dW = C_vdT + PdV = C_vdT + nRdT = C_pdT$

so:
$dS = (C_v + nR)dT/T$

$$\Delta S = \int_{T_1}^{T_2} dS = \int_{T_1}^{T_2} (C_v + nR)dT/T$$

Work out that integral to get the entropy change.

Try to work out parts b, c. and d. using a similar approach.

AM

 

[SwMarc]

Thanks for the help I got them figured out now...I hope