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(B) The work done by a gas during expansion is given by the area under the $P-V$ curve.$(1)$ For isothermal expansion $(a)$,the pressure $P$ decreases

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Case $(b)$

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(B) The work done by a gas during expansion is given by the area under the $P-V$ curve.$(1)$ For isothermal expansion $(a)$,the pressure $P$ decreases as volume $V$ increases according to $P = nRT/V$. The curve is a rectangular hyperbola.$(2)$ For isobaric expansion $(b)$,the pressure $P$ remains constant at $P_i$. The curve is a horizontal line.$(3)$ Since the gas expands from $V_i$ to $V_f$ starting from the same initial pressure $P_i$,the isobaric process maintains the pressure at $P_i$ throughout the expansion,whereas the isothermal process involves a decrease in pressure.$(4)$ Graphically,the area under the horizontal line $(P = P_i)$ from $V_i$ to $V_f$ is a rectangle with area $P_i(V_f - V_i)$. The area under the isothermal curve is smaller because the pressure drops below $P_i$ during the process.$(5)$ Therefore,the work done is greater in the isobaric expansion $(b)$.

$A$. Isobaric	$I$. $\Delta Q = \Delta W$
$B$. Isochoric	$II$. $\Delta Q = \Delta U$
$C$. Adiabatic	$III$. $\Delta Q = 0$
$D$. Isothermal	$IV$. $\Delta Q = \Delta U + P \Delta V$

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