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 at300K. The gas is subjected to a series of reversible, quasi-staticprocesses. For each process, calculate the increase/decrease in theinternal energy of the gas, the work done on or by the gas, and theamount of heat added to or removed from the gas.
1. the gas undergoes an isothermal expansion to a final volume of4x10-3 m3 2. following the expansion, the gas undergoes an isochoric coolingto 200K 3. the gas is then compressed isobarically to a volume of1x10-3 m3 4. a final heating returns the gas to the initial state. theheating is accomplished in such a manner as to produce a straightline on the PV diagram 5. does the gas do net work or have net work done uponit? 6. calculate the efficiency of this engine, or the coefficient ofperformance of this refrigerator, as appropriate
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1. the gas undergoes an isothermal expansion to a final volume of4x10-3 m3 2. following the expansion, the gas undergoes an isochoric coolingto 200K 3. the gas is then compressed isobarically to a volume of1x10-3 m3 4. a final heating returns the gas to the initial state. theheating is accomplished in such a manner as to produce a straightline on the PV diagram 5. does the gas do net work or have net work done uponit? 6. calculate the efficiency of this engine, or the coefficient ofperformance of this refrigerator, as appropriate
I promise to 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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