Question 671: Thermodynamics & KTG

Question

Two moles of an ideal monoatomic gas undergo a cyclic process as shown in figure. The temperatures in different states are given as $6 \mathrm{~T}_1=3 \mathrm{~T}_2=2 \mathrm{~T}_4=\mathrm{T}_3=2400 \mathrm{~K}$. The work done by the gas during the complete cycle is ( $\mathrm{R}=$ Universal gas constant)

Accepted Answer

The $\mathrm{T}-\mathrm{P}$ graph provided in the question can be. converted into a $\mathrm{P}-\mathrm{V}$ diagram as follows:
$$ \begin{aligned} & \quad \begin{array}{l} 1 ightarrow 2: 	ext { Isobaric process } \ 2 ightarrow 3: 	ext { Isochoric process }(	ext { Work done }=0) \ 3 ightarrow 4: 	ext { Isobaric process } \ 4 ightarrow 1: 	ext { Isochoric process }(	ext { Work done }=0) \ \mathrm{T}_1=400 \mathrm{~K}, \mathrm{~T}_2=800 \mathrm{~K}, \ \mathrm{~T}_3=2400 \mathrm{~K}, \mathrm{~T}_4=1200 \mathrm{~K} \ \mathrm{~W}_{1 ightarrow 2}=\mathrm{P}_1\left(\mathrm{~V}_2-\mathrm{V}_1ight)=\mathrm{nR}\left(\mathrm{~T}_2-\mathrm{T}_1ight) \ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\quad=2 \mathrm{R}(800-400)=800 \mathrm{R} \ \quad \begin{aligned} \mathrm{W}_{3 ightarrow 4}=\mathrm{P}_2\left(\mathrm{~V}_4-\mathrm{V}_3ight) & =\mathrm{nR}\left(\mathrm{~T}_4-\mathrm{T}_3ight) \ &\, =2 \mathrm{R}(1200-2400)=-2400 \mathrm{R} \end{aligned} \ 	herefore \quad \mathrm{~W}=\mathrm{W}_{1 ightarrow 2}+\mathrm{W}_{3 ightarrow 4}=-1600 \mathrm{R} \end{array} \end{aligned} $$

Answer

-1600 R

Answer

1600 R

Answer

-1200 R

Answer

800 R

Thermodynamics & KTG

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