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(B) For an ideal gas at constant pressure,the work done $W$ is given by the formula $W = P \Delta V$.Using the ideal gas equation $PV = nRT$,at consta

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$831$

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(B) For an ideal gas at constant pressure,the work done $W$ is given by the formula $W = P \Delta V$.Using the ideal gas equation $PV = nRT$,at constant pressure $P$,we have $P \Delta V = nR \Delta T$.Given:Number of moles $n = 1 \ mol$.Initial temperature $T_1 = 27 \ ^oC = 27 + 273 = 300 \ K$.Final temperature $T_2 = 127 \ ^oC = 127 + 273 = 400 \ K$.Change in temperature $\Delta T = T_2 - T_1 = 400 \ K - 300 \ K = 100 \ K$.Universal gas constant $R = 8.31 \ J/mol-K$.Substituting the values into the work formula:$W = nR \Delta T = 1 	imes 8.31 	imes 100 = 831 \ J$.Thus,the work done is $831 \ J$.

$A$ container having $1 \ mol$ of a gas at a temperature of $27 \ ^oC$ has a movable piston which maintains a constant pressure of $1 \ atm$ in the container. The gas is compressed until the temperature becomes $127 \ ^oC$. The work done is ........ $J$ $(R = 8.31 \ J/mol-K)$.

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