1
$\begingroup$

$1m^3$ of gas undergoes an adiabatic compression from 1 bar to 10 bar. Determine the work required per kg, if its ratio of specific heats is 1.4.

I know that 1 bar is equal $1$x$10^5$Pa. I also know that $PV^k=constant$. I also know that through the adiabatic compression process that work, $w=[m*R*(T2-T1)]/(1-k)$ . I tried using this equation. However how can I calculate the work using this equation if no mass has been specified and no change in temperature?

$\endgroup$
1
  • $\begingroup$ You have to find out "the work required per kg" (citated your own text), thus the mass is known. And so it is enough. Yes, you don't know the temperature change - but you know the pressure change. You have to find another formula on the google. :-) $\endgroup$
    – peterh
    Mar 2 '17 at 17:04
1
$\begingroup$

Adiabatic expansion is the exchange of pressure for volume WITHOUT heat exchange. Therefore any temperature differential is zero. Furthermore there is no loss of material during the expansion/compression, so the mass of the fluid is irrelevant. The work done on compression and during expansion is ideally equal, and is simply the integral of the volume and pressure. Pretty much any thermo textbook will cover the principles. enter image description here

$\endgroup$
2
  • 1
    $\begingroup$ "Therefore any temperature differential is zero" ... what exactly do you mean by that? T2 (after compression) is certainly different from T1 ... as your graph shows. $\endgroup$ Feb 28 '17 at 12:33
  • $\begingroup$ I should have stated without addition or loss of heat energy. $\endgroup$ Feb 28 '17 at 16:19

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.