2 moles of an ideal diatomic gas are initially confined to a volumeof 2x10 -3 m

Question

2 moles of an ideal diatomic gas are initially confined to a volumeof 2x10-3 m3 at 300K. The gas issubjected to a series of reversible, quasi-static processes. Foreach process, calculate the increase/decrease in the internalenergy of the gas, the work done on or by the gas, and the amountof heat added to or removed from the gas.
1. the gas undergoes an isothermal expansion to a final volumeof 4x10-3 m3 2. following the expansion, the gas undergoesan isochoric cooling to 200K 3. the gas is then compressed isobarically to avolume of 1x10-3 m3 4. a final heating returns the gas to theinitial state. the heating is accomplished in such a manner as toproduce a straight line on the PV diagram 5. does the gas do net work or have net workdone upon it? 6. calculate the efficiency of this engine, orthe coefficient of performance of this refrigerator, asappropriate
I promiseto rate you as LIFESAVER if your answer iscorrect!!!
1. the gas undergoes an isothermal expansion to a final volumeof 4x10-3 m3 2. following the expansion, the gas undergoesan isochoric cooling to 200K 3. the gas is then compressed isobarically to avolume of 1x10-3 m3 4. a final heating returns the gas to theinitial state. the heating is accomplished in such a manner as toproduce a straight line on the PV diagram 5. does the gas do net work or have net workdone upon it? 6. calculate the efficiency of this engine, orthe coefficient of performance of this refrigerator, asappropriate
I promiseto rate you as LIFESAVER if your answer iscorrect!!!

Explanation / Answer

Given :             Number of moles (n) = 2 moles .             Initial volume (v1)   = 2 x 10-3 m3              Temperature(T) = 300 K (a)           Workdone in Isothermal expansion is :                            W   = n R T   log ( v2 /v1)      Where R = Universal gas constant.                                   = 2 * 8.314 *300 log ( 4 x10-3 /  2 x 10-3 )                                   =   --------------- J (b)           InIsochoric process , volume is constant .                      Work   dW   = P.dv                                           = 0 J (c)       W   = P .dv              = 1 atm * (2 - 1) * 10-3   m3 (d)           The gaedo net workdone. (e)          Efficiency is:   W / Q = 1 - T2 / T1         coefficient ofperformance of this refrigerator is :  K   = Q / W Hope this helps u!              Temperature(T) = 300 K (a)           Workdone in Isothermal expansion is :                            W   = n R T   log ( v2 /v1)      Where R = Universal gas constant.                                   = 2 * 8.314 *300 log ( 4 x10-3 /  2 x 10-3 )                                   =   --------------- J (b)           InIsochoric process , volume is constant .                      Work   dW   = P.dv                                           = 0 J (c)       W   = P .dv              = 1 atm * (2 - 1) * 10-3   m3 (d)           The gaedo net workdone. (e)          Efficiency is:   W / Q = 1 - T2 / T1         coefficient ofperformance of this refrigerator is :  K   = Q / W Hope this helps u!

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