Thermodynamics hw question

[andytran]

Hi,

i'm stuck on this question for my hw, please do give any advice/suggestions .. thanks!


For Berthelot equation of state P = RT/(v-b) - a/(Tv^2)

where T is the thermodynamic temp, a and b are constants, R is the Universal gas constant.

a) Show that Lim_(T->infinity) v/T = R/P
(just to be clear, it's the limit of v/T where T goes to infinity is equal to R/P)

thanks again!

 

[andytran]

nvm solved it. thanks for viewing anyway...

 

[quicknote]

Hello,

Thank you for reaching out for help with your homework question. The Berthelot equation of state is a mathematical representation of the relationship between pressure, volume, and temperature for a gas. In this equation, a and b are constants that depend on the gas being studied, and R is the Universal gas constant.

To show that Lim_(T->infinity) v/T = R/P, we can start by rearranging the equation to solve for v/T:

v/T = (RT/P) - (a/P)(1/Tv^2)

Next, we can take the limit as T approaches infinity. As T gets larger and larger, the second term on the right side of the equation will approach zero, leaving us with:

Lim_(T->infinity) v/T = RT/P

Finally, we can substitute in the value for R/P, which is a constant, to get:

Lim_(T->infinity) v/T = R/P

I hope this explanation helps and that you are able to successfully solve your homework question. Remember to always check your work and double check your units to ensure you have the correct answer. Good luck!