# Need assitance re: Internal energy calculations on Polytropic expansion

#### Darkane

Hi everyone,

I'm having an issue with a question I'm trying to solve. Here is the question:

A gas with an initial pressure of 800Kpa, 0.02m3 expands following a polytropic process. The final conditions are 350Kpa, 0.042m3. Find the following:

a) Index of expansion
b) Work done
c) Change in Internal Energy
d) Heat transfer

I'm stuck on c). If someone could guide me through it would be of help.

a) n = 1.11 using P1/P2 = (V2/V1)^n
b) 11.82KJ using P1V1-P2V2/n-1

Why I'm stuck: During my studies I've found internal energy to be only tied to temperature. What am I missing?

Thanks gentlemen.

#### THERMO Spoken Here

The idenity of the gas and its critical properties are not stated. The mass is not known.

The idea "Polytropic" is most commonly used with the system substance assumed to be an ideal gas. In general internal energy of a simple compressible substance has dependence: u = u(T,v). In actuality, as space expands, pressure diminishes or temperature rises - or in combination... the internal energy comes to depend on temperature only u = u(T).

To understand, one must sketch the event on p-v coordinates. Work is the area under
the curve. The change of internal energy is cv(T2-T1). Put the work and the IE change into the energy equation.

Good Luck

Blowgun Hunter | THERMO Spoken Here!

• 1 person

#### THERMO Spoken Here

polytropic - say what?

I now recall I sumarized the classical idea "polytropic" at my site.

Here is my perspective of "what it is!"
C:\Users\Jim\a_ROOT\wp\03_tsh\C6100_3.20_polytropic\polytropic.html

Good Luck again... JP

#### Darkane

The idenity of the gas and its critical properties are not stated. The mass is not known.

The idea "Polytropic" is most commonly used with the system substance assumed to be an ideal gas. In general internal energy of a simple compressible substance has dependence: u = u(T,v). In actuality, as space expands, pressure diminishes or temperature rises - or in combination... the internal energy comes to depend on temperature only u = u(T).

To understand, one must sketch the event on p-v coordinates. Work is the area under
the curve. The change of internal energy is cv(T2-T1). Put the work and the IE change into the energy equation.

Good Luck

Blowgun Hunter | THERMO Spoken Here!
Thanks for the response. Here is my issue: without a Cv I can't solve.

I can use the P-V-T relationships to sub out DeltaT but can't solve. I can create a Cv using R: 8.314 but can I substitute gamma for my N index?

I still don't see it using the fundamental equation. Cv is my hold up.

#### THERMO Spoken Here

You are correct - I over-looked the cv necessity. The problem statement is incomplete. How would one know so much without knowing the gas species?
No answer possible without a guess. So you can say:

If monatomic cv = 3/2(R/M) and...
or if diatomic cv = 5/2(R/M) and ...

Actually you don't know the molecular species so ???????