Adiabatic Irreversible Compression of an Ideal Gas It does not seemgenerally t o be recognized that, for an ideal gas, there is alimit below which the volume cannot be teduced by ane-stage adiabatic compression, whatever be the external pressure. Let us consider one mole of an ideal gas, initially occupying a volume VI, the pressure and temperature being PI and TI, respectively. Let the gas be adiabatically compressed by a constant external pressure Pz till the gas pressure becomes equal to P2, the final volume and temperature of the gas being Vz and T2, respectively. Let Vz = xV1,where x is a fraction. By considering the work done in this single-stage adiabatic compression, and assuming C, and C, to be independent of temperature, it can he shown that, for an ideal gas
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Since C, and C, are positive, andP2 2 PI,then 1 r 2 RIC,. Hence x approaches a limiting value of RIC,, as PdP, increases without bound. Conseauentlv. ,. TI . m as P, m. F18ran i d 4 rnonstvmic gar C, = 5 HZ,and hence x > 215, i.e, surh a gas cannot be adiatudcallg compressed ro lrss than two-filthpol irsoriginalwlume (\',I inasinglestagc, however large rhecxrernal pressure ( P A )Thelrmmng . rnlur of x is obviourly mdrprndent of the mitinl srateof thegat For a polyarnm~cideal gas, the limiting value of x uill be lower, siner C, is larger than 512R. It must be distinctly understood that a limiting value of x exists only for single-stage adiabatic compression by application of a constant external pressure (P2). By multistage compression, and obviously by a reversible process i t is a t least theoretically possible to compress an ideal gas adiabatically to any desired volume.
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Mlhlr Nalh Das Jadavpur University Calcuna-700032, India
Volume 63
Number 1 January 1986
27
