Three moles of an ideal monatomic gas performs a cyclic process as shown in figure. temperatures in

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11.Thermodynamics

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Three moles of an ideal monatomic gas performs a cyclic process as shown in the figure. The temperatures in different states are $T_1 = 400\,K, T_2 = 800\,K, T_3 = 2400\,K$ and $T_4 = 1200\,K$. Determine the work done by the gas during the cycle .... $kJ$ [Given $R = 8.31\, J-mole^{-1}K^{-1}$)

A

$19.94$

B

$22.65$

C

$15.81$

D

$10.37$

Solution

$\mathrm{W}=\mathrm{W}_{12}+\mathrm{W}_{23}+\mathrm{W}_{34}+\mathrm{W}_{41}$

$=0+\mathrm{nR}\left(\mathrm{T}_{3}-\mathrm{T}_{2}\right)+0+\mathrm{nR}\left(\mathrm{T}_{1}-\mathrm{T}_{4}\right)$

$=\mathrm{nR}\left[\left(\mathrm{T}_{3}+\mathrm{T}_{1}\right)-\left(\mathrm{T}_{2}+\mathrm{T}_{4}\right)\right]$

$=3 \times 8.31[(2800)-(2000)] J$

$=19944 \mathrm{J}$

Standard 11

Physics

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