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CHXI06:THERMODYNAMICS

369390 An ideal gas on isothermal reverisble compression from $10 L$ to $5 L$ performs $1730 J$ of work at $300 K$ . Calculate the number of moles of gas involved in compression? $(R = 8.314 J K^{- 1} {mol}^{- 1})$

1 2.5

2 2

3 1

4 3

Explanation:

$V_{1} = 10 L, V_{2} = 5 L, W = 1730 J$ ,
$T = 300 K, R = 8.314 J K^{- 1} {mol}^{- 1}, n = ?$
Workdone in isothermal reversible compression, $W_{max} = - 2.303 nRT \log_{10} \frac{V_{2}}{V_{1}}$
$∴ 1730 J = - 2.303 \times n \times 8.314 J K^{- 1} m o l^{- 1} \times$
$300 K \times \log_{I 0} (\frac{5}{10})$
$∴ n = \frac{1730 J}{(\begin{matrix} - 2.303 \times 8.314 J K^{- 1} mo l^{- 1} \times \\ 300 K \times \log_{10} (0.5) \end{matrix})}$
$∴ n = \frac{1730}{- 5744.14 \times (- 0.3010)} mol$
$∴ n = \frac{1730}{1729} \approx 1 mol$

MHTCET - 2021

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