Question 160: Thermodynamics & KTG

Question

A real gas within a closed chamber at $$27^{\circ} \mathrm{C}$$ undergoes the cyclic process as shown in figure. The gas obeys $$P V^3=R T$$ equation for the path $$A$$ to $$B$$. The net work done in the complete cycle is (assuming $$R=8 \mathrm{~J} / \mathrm{mol} \mathrm{K}$$):

Accepted Answer

For $A$ to $B$ :
Given $\mathrm{PV}^3=\mathrm{RT} \Rightarrow \mathrm{P}=\frac{\mathrm{RT}}{\mathbf{V}^3}$
Work done $\mathrm{W}_{\mathrm{AB}}=\int \mathrm{PdV}$
$\begin{aligned} & =\int \frac{R T}{V^3} d V=R T\left[\frac{V^{-2}}{-2}ight]_{V_1=2}^{V_B=4} \\ & =-\frac{R T}{2}\left[\frac{1}{V^2}ight]=-\frac{R T}{2}\left[\frac{1}{16}-\frac{1}{4}ight] \\ & =-\frac{R T}{2}\left(\frac{-3}{16}ight)=\frac{3 R T}{32}\end{aligned}$
$\begin{aligned} & =\frac{3}{32} 	imes 8 	imes 300=225 \mathrm{~J} \\ & \mathrm{~W}_{\mathrm{B} . \mathrm{C}}(	ext { Isobaric process ) } \\ & \mathrm{W}_{\mathrm{BC}}=\mathrm{P} \Delta \mathrm{V}=10(2-4)=-20 \mathrm{~J} \\ & \mathrm{~W}_{\mathrm{B} . \mathrm{C}}(	ext { Isochoric process })=0 \\ & \mathrm{~W}_{	ext {nct }}=\mathrm{W_{AB}}+\mathrm{W}_{\mathrm{BC}}+\mathrm{W}_{C A}=225-20+0=205 \mathrm{~J}\end{aligned}$

Answer

$$-20$$J

Answer

205J

Answer

225J

Answer

20J

Thermodynamics & KTG

A real gas within a closed chamber at $27^{\circ} \mathrm{C} undergoes the cyclic process as shown in figure. The gas obeys P V^3=R T equation for the path A to B. The net work done in the complete cycle is (assuming R=8 \mathrm{~J} / \mathrm{mol} \mathrm{K}$):

Choose the correct answer: