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Properties of Enthalpy

Six moles of ...

Question

Six moles of an ideal gas performs a cycle shown in figure. The temperatures are $T_{A} = 600 K, T_{B} = 800 K, T_{C} = 2200 K$ and $T_{D} = 1200 K$ . The work done by the cycle $A B C D A$ is

A

20 k J

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B

30 k J

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C

40 k J

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D

60 k J

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Solution

The correct option is B $40 k J$
Given, $n = 6$
AB $:$ isochoric process, $Δ W_{A B} = 0$
BC $:$ isobaric process, $Δ W_{B C} = n R Δ T$
$= n R (T_{c} - T_{a})$
$= 6 R (2200 - 800)$
$= 8400 R$
CD $:$ isochoric process, $Δ W_{C D} = 0$
DA $:$ isobaric process, $Δ W_{D A} = n R Δ T$
$= n R (T_{A} - T_{D})$
$= 6 R (600 - 1200)$
$= - 3600 R$
$Δ W_{c y c l i c} = Δ W_{A a} + Δ W_{a c} + Δ W_{C o} + Δ W_{D A}$
$= 8400 R - 3600 R = 4800 R$
$= 4800 \times 8.3$
$= 39840 J \equiv 40$ kJ.

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