Thermo question, two methods of changing volume/temp

does this look right?

for the quasistatic case you can use thermodynamics to find the temperature at any time,

for the other case you have to use dU=dW and so on since its not quasistatic

 

Oh right,

so the quasistatic case should be:

T_f=P_fV_f/(NK_B)

for some reason i forgot that the pressure was changing in that case as well,

this makes more sense, in the quasistatic case you can find the state of the system at any point in terms of the state variables, and P is one of those too!

thanks ehild =]

 

quasistatic case :

T_f=P_fV_f/(NK_B)

under constant pressue:

T_f=2P_ex(Vi-Vf)/3Nk_B + Ti

 

Oh,

do you mean something like



where gamma is the ratio of heat capacities under constant pressure / volume?

 

yea theres afew like

TV^(gamma - 1)=constant

PV^gamma = const

but wouldnt mucking around with these and introducing them into my problem make it like

Tf=PfVf/(NKB)=P_iV_f^1-λVi^λ/(NK_B)

using λ as gamma

PV^gamma = const = C say



Tf=CV_f^1-λ/NK_B

then i have this unknown constant C

 

C=NKb Tf Vf^(γ-1)=NKb TiVi^(γ-1)


Tf= Ti(Vf Vi)^(γ-1)

for γ=Cp/Cv

Tf= Ti(Vf Vi)^(Cp/Cv-1)

is that kind of what you mean?

 

oh whoops,


T_f=T_i(V_i/V_f)^5/3-1.



T_f=T_i(V_i/V_f)^2/3.

thanks ehild