Calculate the work done if 1 mole of an idea | vedclass

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(A) For an isothermal reversible compression of an ideal gas,the work done $(w)$ is given by the formula: $w = -2.303 \ nRT \log\left(\frac{V_f}{V_i}\

Vedclass · Accepted Answer

$1.729$

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(A) For an isothermal reversible compression of an ideal gas,the work done $(w)$ is given by the formula: $w = -2.303 \ nRT \log\left(\frac{V_f}{V_i}ight)$.Given: $n = 1 \ mol$,$R = 8.314 \ J \ K^{-1} \ mol^{-1}$,$T = 300 \ K$,$V_i = 12 \ dm^3$,$V_f = 6 \ dm^3$.Substituting the values: $w = -2.303 	imes 1 	imes 8.314 	imes 300 	imes \log\left(\frac{6}{12}ight)$.$w = -2.303 	imes 8.314 	imes 300 	imes \log(0.5)$.Since $\log(0.5) = -0.3010$,we have: $w = -2.303 	imes 8.314 	imes 300 	imes (-0.3010)$.$w \approx 1728.8 \ J = 1.729 \ kJ$.

Calculate the work done if $1 \ mole$ of an ideal gas is compressed isothermally and reversibly from $12 \ dm^3$ to $6 \ dm^3$ at $300 \ K$. $\left[R = 8.314 \ J \ K^{-1} \ mol^{-1}\right]$ (in $kJ$)

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