How to Solve for Volume and Temperature in a Thermodynamic Problem?

[Nguyenfa.t]

Homework Statement

The problem is on the attachment. I can't seem to find the volume or temperature of T. If someone can tell me how to find them i can do the rest of the problem. Any help would be greatly appreciated.

Homework Equations

The Attempt at a Solution

on the attachment

 

[kuruman]

You say you can't seem to find the volume or temperature. What have you tried? What equations did you start from?

 

[Nguyenfa.t]

i used the PV= NRT

I can't find the Volume and Temperature of point C only.

 

[kuruman]

I will not be able to offer any suggestions until I can open your attachments.

 

[Nguyenfa.t]

Well the problem is

One mole of a diatomic ideal gas has a pressure of 8atm and a volume of 3 L at point A. The gas is then expanded isothermally to point B where the volume is 12 L. The gas is then compressed isobarically to point C. the gas is returned to point A via an adiabatic compression. Depending on the calculation assume that R is 8 J/Mol (K) or .08 L atm/ mol K

 

[kuruman]

I can see the attachments now. You are given the volume, pressure, number of moles and R. Can you find the temperature at point A?

 

[Nguyenfa.t]

yes i found the temp of A and B because they are the same since they are isothermal. knowing that i could find the Pressure of B and C because they are isobaric, but i can't find the volume or temp of point C.

 

[kuruman]

OK. Now there is an equation that relates point A to point B and one that relates point A to point C. What are these equations?

 

[Nguyenfa.t]

I don't know what equations and how do they relate? by going back to a via adiabatic process doenst that mean no heat is transferred?

 

[kuruman]

Yes, adiabatic means no heat is transferred. Also, for the adiabatic process,

p_AV_A^γ = p_CV_C^γ

where γ = C_P/C_V

Find γ for a diatomic gas, then use this relation to find V_C.

 

[Nguyenfa.t]

so Cp/Cv= 7/2R divided by 5/2R? where R is .08?

 

[Nguyenfa.t]

and then what do i do? can you show me please?

 

[Nguyenfa.t]

i get y= 1.4 then what do i do?

 

[kuruman]

Use the relation I gave you earlier to find V_C. You know everything else. Once you have V_C, you can find T_C.

 

[Nguyenfa.t]

i get Vc^1.4= 42.8 how do i solve that? can anyone else help?

 

[queenofbabes]

Surely you know logarithms?

 

[Nguyenfa.t]

is it ln 42.8= 1.4? but then what do i solve?

 

[kuruman]

You can rewrite 1.4 as 7/5. You get

V_C^7/5=42.8

Raise both sides of the equation to the 5/7 power. This gives you

(V_C^7/5)^5/7=42.8^5/7

Can you get a number for V_C now?