If 5 moles of an ideal gas expands from 10L to a volume of 100L at...

If $5$ moles of an ideal gas expands from $10L$ to a volume of $100L$ at $300K$ under isothermal and reversible condition then work, $w$ , is $- xJ$ . The value of $x$ is $-$ _______.

(Given $R = 8 .314 J{K}^{- 1}{mol}^{- 1}$ )

Correct answer

Step-by-step solution

Given,

$T = 300K, {V}_{1} = 10L, {V}_{2} = 100L, n = 5$

It is isothermal reversible expansion, so work done negative

$W = - 2 .303 nRTlog\left(\dfrac{{V}_{2}}{{V}_{1}}\right)$

$= - 2 .303 \times 5 \times 8 .314 \times 300\log \left(\dfrac{100}{10}\right)$

$= - 28720 .713 J$

$≡ - 28721J$

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