A thermodynamic process is shown in the figure. The pressures and volumes corresponding to some points in the figure are :
${P_A} = 3 \times {10^4}Pa,\;{P_B} = 8 \times {10^4}Pa$ and ${V_A} = 2 \times {10^{ - 3}}{m^3},\;{V_D} = 5 \times {10^{ - 3}}{m^3}$
In process $AB$, $600 J$ of heat is added to the system and in process $BC, 200 J $ of heat is added to the system. The change in internal energy of the system in process $ AC$ would be ...... $J$
AIPMT 1992, Diffcult
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(a) By adjoining graph ${W_{AB}} = 0$ and
${W_{BC}} = 8 \times {10^4}[5 - 2] \times {10^{ - 3}} = 240\,J$
${W_{AC}} = {W_{AB}} + {W_{BC}} = 0 + 240 = 240\,J$
Now, $\Delta {Q_{AC}} = \Delta {Q_{AB}} + \Delta {Q_{BC}} = 600 + 200 = 800\,J$
From FLOT $\Delta {Q_{AC}} = \Delta {U_{AC}} + \Delta {W_{AC}}$
==> $800 = \Delta {U_{AC}} + 240$ ==> $\Delta {U_{AC}} = 560\,J.$
${W_{BC}} = 8 \times {10^4}[5 - 2] \times {10^{ - 3}} = 240\,J$
${W_{AC}} = {W_{AB}} + {W_{BC}} = 0 + 240 = 240\,J$
Now, $\Delta {Q_{AC}} = \Delta {Q_{AB}} + \Delta {Q_{BC}} = 600 + 200 = 800\,J$
From FLOT $\Delta {Q_{AC}} = \Delta {U_{AC}} + \Delta {W_{AC}}$
==> $800 = \Delta {U_{AC}} + 240$ ==> $\Delta {U_{AC}} = 560\,J.$
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