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(B) For an isobaric process (constant pressure),the work done is given by $W = P \Delta V$.Using the ideal gas equation $PV = nRT$,for a constant pres

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$814$

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(B) For an isobaric process (constant pressure),the work done is given by $W = P \Delta V$.Using the ideal gas equation $PV = nRT$,for a constant pressure process,$P \Delta V = nR \Delta T$.Given: $n = 1 \, mol$,$T_1 = 27^{\circ}C = 300 \, K$,$T_2 = 127^{\circ}C = 400 \, K$.Change in temperature $\Delta T = T_2 - T_1 = 400 - 300 = 100 \, K$.Using $R = 1.987 \, cal/mol-K$ (since $C_P$ is given in $cal$),$W = nR \Delta T = 1 	imes 1.987 	imes 100 = 198.7 \, cal$.To convert work from calories to Joules,we use $1 \, cal \approx 4.184 \, J$.$W = 198.7 	imes 4.184 \approx 831.4 \, J$.Comparing with the given options,the closest value is $814 \, J$.

$A$ container having $1$ mole of a gas at a temperature $27^{\circ}C$ has a movable piston which maintains a constant pressure in the container of $1 \, atm$. The gas is compressed until the temperature becomes $127^{\circ}C$. The work done is ........ $J$ ($C_P$ for the gas is $7.03 \, cal/mol-K$).

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