The figure shows two paths that may be taken by a gas from an initial point i to final point f. Path 1 consists of an isothermal expansion (work is 50 J in magnitude), an isothermal compression (work is 30 J in magnitude), an adiabatic expansion (work is 40 J in magnitude) and then an adiabatic compression (work is 25 J in magnitude). Find the magnitude of change in internal energy (in J) in path 2, i.e., in path AFGE.

Question

The figure shows two paths that may be taken by a gas from an initial point i to final point f. Path 1 consists of an isothermal expansion (work is 50 J in magnitude), an isothermal compression (work is 30 J in magnitude), an adiabatic expansion (work is 40 J in magnitude) and then an adiabatic compression (work is 25 J in magnitude). Find the magnitude of change in internal energy (in J) in path 2, i.e., in path AFGE. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Δ UA B+Δ UB C+Δ UC D+Δ UD E=Δ Ui f 0+(-WB C)+0+(-WD E)=Δ Ui f -40 J +(-(-25))=Δ U-i f -40+25=Δ U-i f Δ Ui f=-15 J (For path A B: Isothermal process .QA B=WA B=50 J )

ΔUAB​+ΔUBC​+ΔUCD​+ΔUDE​=ΔUif​ 0+(−WBC​)+0+(−WDE​)=ΔUif​ −40J+(−(−25))=ΔU−if​ −40+25=ΔU−if​ ΔUif​=−15J (For path AB : Isothermal process QAB​=WAB​=50J)

$Δ U_{A B} + Δ U_{BC} + Δ U_{C D} + Δ U_{D E} = Δ U_{i f}$
$0 + (- W_{BC}) + 0 + (- W_{D E}) = Δ U_{i f}$
$- 40 J + (- (- 25)) = Δ U_{- i f}$
$- 40 + 25 = Δ U_{- i f}$
$Δ U_{i f} = - 15 J$
(For path $A B$ : Isothermal process
$Q_{A B} = W_{A B} = 50 J)$