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Explain the isobaric process and derive the work done in this process. |
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Answer» <P> Solution :Isobaricprocess : thisis a thermodynamicprocessthat occursat constantpressure.eventhrough pressureis CONSTANTIN this process , temperature, volumeand internalenergyare not constant. Fromthe idealgas equationwe have` V= ((mu R )/( P ))T `...(1) Here`(mu R) /( P)= ` constant In an isobaricprocessthe temperatureis directly proportionalto volume. ` V porpT ` ( Isobaricprocess ) THisimpliesthat fora isobaricprocess, theV-Tgraphis astraightlinepassingthroughthe origin. IF agasgoesfroma state`(V_i , T_i ) `to` (V_f , T_f)`at constantpressurethen thesystemsatisfiesthefollowinngequation ` (T_f )/(V_f )=(T_i )/(V_i)` Examplesfor Isobaricprocess : ( i ) whenthe gasheated andpushes thepiston so thatit exertsa forceequivalent toatmosphericpressureplusthe forcedueto gravity then this process is isobaric . (ii )Mostof thecookingprocesses in ourkitchenare isobaricprocesses , whenthe foodis cookedin an openvesselthepressureabovethefoodis alwaysat atmosphericpressure The PVdiagramfor anisobaricprocessis a horizontallineparallelto volumeaxisfigure(a)representsisobaricproceesswheredecreases figure(b)representsisobaricprocesswherevolumeincreases  The workdonein an isobaricprocess : workdoneby thegas ` W= int_(v_1)^(v_f)pd V ` In an isobaricprocess the pressureis constant, soP comesoutoftheintegral ` W= P int_(v_i)^(v_f) DV ` ` W=P[V_f -V_i]=P Delta V ` Where`Delta V `denoteschange in thevolume.IF`Delta V ` isnegative ,Wis alsonegativethisimpliesthat theworkis doneon thegas.If ` Delta V `is positive, Wis positiveW isalsopositiveimplying that workis done by thegas . Theequation(6)can ALSOBE rewrittenusingtheidealgasequation. fromidealgasequation ` PV = mu RTand V =( mu RT )/(P )` Substitutingthis inequation( 6)we get `W = mu RT_f(1- (T_i )/(T_f ))` inthePVdiagram, areaunderthe isobariccurveis equalto theworkdoneis isobaricprocess .  Thefirstlaw ofthermodynamics forisovaricprocessis givenby ` DeltaU =Q- P Delta V ` ` W = P DeltaV ,Delta U = Q- mu RT _f [ 1-(T_i )/(T_f)]` |
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