# Directions: Question are based on the following paragraph.Two moles of helium gas are taken over the cycle $\dpi{100} ABCDA$, as shown in the $\dpi{100} P-T$ diagram.Question: The work done on the gas in taking it from  $\dpi{100} D\; to\; A$ Option 1) $-414R\; \;$ Option 2) $\; \; +414R\;$ Option 3) $\; -690R\;$ Option 4) $\; +690R$

As we leant in

Work Done for Isothermal Reversible Compression of an ideal gas -

$W= -nRT\ln \frac{V_{f}}{V_{i}}$

$V_{i}> V_{f}$

- wherein

At constant temperature

$P\, \alpha \frac{1}{V}$

$W= -nRT\, \ln \frac{P_{i}}{P_{f}}$

$P_{f}> P_{i}$

$W_{DA}= 2.3 \ n R {T} \log \frac{P_{1}}{P_{2}}=-(2.302) (2) (R) (300) \log \left( \frac{1\times 10^{5}}{2\times 10^{5}}\right )$

$= + (2.3) (600R) (0.3) = 414R$

Option 1)

$-414R\; \;$

Incorrect

Option 2)

$\; \; +414R\;$

Correct

Option 3)

$\; -690R\;$

Incorrect

Option 4)

$\; +690R$

Incorrect

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