# Calculating the change in entropy of an ideal gas under compression

## Homework Statement

Initial
pressure: 140kPa
Temperature: 25C or 298K
Volume: 0.14m^3

Final
Pressure:1.4MPa or 1400kPa

It uses index compression, n=1.25. So PV^1.25 = constant.

c_p = 1.041kJ/kg.K and c_v = 0.743 kJ/kg.K

## Homework Equations

¥ = c_p/c_v
ΔS=c_v*ln(Tf/Ti) + R*ln(Vf/Vi) [i think]

## The Attempt at a Solution

I found ¥ to be 1.4012
PV^n = 12 therefore Vf = 0.0222

140*0.14^1.25=11.989
1400*Vf^1.25=11.989
Vf^1.25=11.989/1400

PeterDonis
Mentor
2020 Award
So far your work looks OK. Where are you stuck?

So far your work looks OK. Where are you stuck?
hi,

So where do i use the Vf? I don't I use "ΔS=c_v*ln(Tf/Ti) + R*ln(Vf/Vi) " as part two asks for the final temperature. So part one wants me to find the entropy, but i dont know how to do this.

PeterDonis
Mentor
2020 Award
Are there any other equations that involve the entropy? For example, for the special case (which it seems would apply to your problem) where the gas does not exchange heat with the environment?

Chestermiller
Mentor
I don't see any problem with solving for the final temperature first and then substituting for the delta S. Alternately, you can solve for the temperature ratio in terms of the volume ratio by combining the polytropic relationship with the ideal gas law:
##\Delta lnT-\Delta lnV=\Delta lnP##
##n\Delta ln V=-\Delta lnP##

Solve for ##\Delta lnV## and ##\Delta lnT## in terms of ##\Delta lnP##

Chet

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