Question

3.19 A gas with adiabatic exponent γ is compressed adiabatically from an initial state (Pi, Vi) to final state (Pf, Vf). (a) Show that the work done in this process is

W=((ViPi)/y-1)*[(Vi/Vf)^(y-1) -1]

(b) Evaluate the result numerically for one mole of helium gas initially
at P = 1.0 atm and T = 300 K compressed to half its initial volume.
(c) Compute the work done in an isothermal compression from the same
initial point to half the initial volume. Explain the difference between
the numerical results for work done in adiabatic and isothermal
compression.

Answer 1

As we can see the Work done results for both the processes, we can say that the Adiabatic compression work is larger than the isothermal compression work.

Because...compression lowers the volume of the system and therefore usually increases the temperature when heat exchange with the surroundings is not allowed(adiabatic compression). Whereas, Isothermal compression requires heat transfer to the surroundings to maintain constant temperature, lowering the pressure of the system and thus lowering the resistance to compression compared to the adiabatic compression (where heat exchange is not allowed).

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