Two moles of helium gas undergo a reversible cyclic process as shown in figure. Assuming gas to be ideal, what is the net work involved in the cyclic process?

- 100 R l n 4

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+ 100 R l n 4

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+ 200 R l n 4

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- 200 R l n 4

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Solution

The correct option is A $- 100 R l n 4$
At constant temperature & pressure
Volume of $C_{3} H_{8} = 36.5 m l$
Volume of $C H_{4} + C O = 100 m l - 36.5 m l = 63.5 m l$
Combustion reactions,
$C_{3} H_{8} + 5 O_{2} ⟶ 3 C O_{2} + 4 H_{2} O$
$C H_{4} + 2 O_{2} ⟶ C O_{2} + 2 H_{2} O$
$C O + 1 / 2 O_{2} ⟶ C O_{2}$
$1$ mole $C_{3} H_{8}$ produce $3$ moles of $C O_{2}$
$1$ mole of $C H_{4}$ & $C O$ each form $1$ mole $C O_{2}$
or in mls, $C O_{2} = 3 \times 36.5 + (100 - 36.5)$
$= 109.5 + 63.5 = 173 m l$ of $C O_{2}$

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