The work done when $1 ext{ mole}$ of gas expands reversibly and isothermally from a pressure of $5 ext{ at

Question

The work done when $1 	ext{ mole}$ of gas expands reversibly and isothermally from a pressure of $5 	ext{ atm}$ to $1 	ext{ atm}$ at $300 	ext{ K}$ is: [Given: $\log 5 = 0.6989$ and $R = 8.314 	ext{ J K}^{-1} 	ext{ mol}^{-1}$]

Accepted Answer

For an isothermal reversible expansion of an ideal gas, the work done ($w$) is given by the formula:
$w = -2.303 nRT \log\left(\frac{p_i}{p_f}ight)$
Given data:
Number of moles, $n = 1 	ext{ mole}$
Temperature, $T = 300 	ext{ K}$
Initial pressure, $p_i = 5 	ext{ atm}$
Final pressure, $p_f = 1 	ext{ atm}$
Gas constant, $R = 8.314 	ext{ J K}^{-1} 	ext{mol}^{-1}$
$\log 5 = 0.6989$
Substituting the values into the formula:
$w = -2.303 	imes 1 	imes 8.314 	imes 300 	imes \log\left(\frac{5}{1}ight)$
$w = -2.303 	imes 2494.2 	imes \log 5$
$w = -5744.14 	imes 0.6989 \approx -4014.6 	ext{ J}$
The negative sign indicates that work is done by the system (expansion) .

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