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Shweta thakur Asked a Question September 17, 2020 10:20 pm 30 pts uring the opctaton, an amount of heat , exactly equal to w, will be returned to the sink at theat has been giet tc SStem. smg the appropriate conventions of sign, 4 Wil be negauv . Isothermal Expansion. The cylinder containing one Re ok the ideal gas, occupying a volume , is placed in contact 2t tae souree (e, heat reservoir at temperature 7,). The ga atsorhs heat , from the source and expands isothermally and versibiy till its volume has increased to The path of the pocess is representod by the isothermal curve AB Snce the 8as is ideal, the wvork done, w, by one mole of the ideal gas will be given by ACV 5 will be poSitive so that BV 1sOTHERMAL (T2 - RT, In IV. Adiabatie Compression. The cylinder is now removed from the sink and placed agan o oNASOTHERMAL sulating nmatertat. ne gas is then compressed adiabatically and reversibly along DA till the initat stiate 4 insula regained. The temperature of the gas rises from 7 to T, The work done is positive by the conventons cV L (T) s (6) - RT In (1) sign and Wlt be given by w =C, (7-7) Further, for an ideal gas, the work done is equal to the heat absorbed, 9, So that VOLUME As a result of these four operations, the system has returned to its original state so that a reversible eyc FIGURE 2.1. Carnot cycle. has been compietcd. he net work OP) done by the system will be given by -4 RT, In Here, has been taken as egative and 92 a5 pOsz{ive by the latest SI conventions of sign. -RT, I-c, (7,-7)+RT, ln+C, -7) INSULATION 8) = RT, ln+ RT, In 1 Since and lie on one adiabatic curve and V and V lie on another, it follows that V /3 (10) 2 and sOURCE AT T2 INSULATION MATERIAL SINK AT T1 INSULATION MATERIAL Comparing cquations (9) and (10), we get FIGURE 2.2. Different operations of the Carnot cycle. (- IL Adiabatic Expansion. The cylinder is now removed from the source and placed in perfectly insulating material so that the gas now expands adiabatically and reversibly. Work is done in the expansion but since no heat enters or leaves the system, the temperature must fall. The reversible adiabatic expansion is continued till the temperature has fallen to 7, which is the temperature of the sink. Suppose the corresponding volume becomes3 The path is shown by the adiabatic curve BC in Fig. 2.1. The work done w, Will be given by (11) Putting this value in cquation (8), we get V2 RT, In+ RT, In RT, In - Rr, ln V -W C, (7-7,) =-C, T -T7) 3) = R (T-71) In here is the heat capacity of the ideal gas. Here, again w, is negative by the usual conventions of sign. Dividing equation (12) by equation (2), we get IL Isothermal Compression. The cylinder is now removed from the insulating material andplaced in ntact with the sink (i.e., the heat reversoirat the lower temperature 77). The gas is compressed isothermally i reversibly till the volume decreases from V to V. The process is represented by the path CD in F1g. 2.1. work done is taken as positive by the usual conventions of sigr and hence will be given by which gives the efficiency of the Carnot cycle or engine, .4) " = RT, In THERMODYNAMICS II Pradeep's PHYSICAL CHEMISTRY VOL. 11

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