10 , mol of an ideal gas expands isothermally | vedclass

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(B) The work done in an isothermal reversible expansion is given by $W = -2.303 \, nRT \log_{10} \left( \frac{P_1}{P_2} \right)$.Substituting the give

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$58.55$

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(B) The work done in an isothermal reversible expansion is given by $W = -2.303 \, nRT \log_{10} \left( \frac{P_1}{P_2} ight)$.Substituting the given values: $W = -2.303 	imes 10 	imes 8.314 	imes 300 	imes \log_{10} \left( \frac{10}{1} ight)$.$W = -2.303 	imes 10 	imes 8.314 	imes 300 	imes 1 = -57441.4 \, J$.The magnitude of work available is $57441.4 \, J$.This energy is used to lift a mass $m$ to a height $h = 100 \, m$,so $W = mgh$.$57441.4 = m 	imes 9.8 	imes 100$.$m = \frac{57441.4}{980} \approx 58.61 \, kg$.

$10 \, mol$ of an ideal gas expands isothermally and reversibly from a pressure of $10 \, atm$ to $1 \, atm$ at $300 \, K$. What is the largest mass (in $kg$) which can be lifted through a height of $100 \, m$ by the energy obtained in this process (in $, kg$)?

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