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(C) For an ideal gas, the equation of state is $PV = nRT$. An isotherm is a process where the temperature $T$ remains constant. Since $n$ and $R$ are

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$C$

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(C) For an ideal gas, the equation of state is $PV = nRT$. An isotherm is a process where the temperature $T$ remains constant. Since $n$ and $R$ are constants, for an isotherm, $PV = 	ext{constant}$. Given initial conditions: $P_i = 3$ and $V_i = 4$. Therefore, the product $P_i V_i = 3 	imes 4 = 12$. We check the product $PV$ for each process:Process $A$: $P 	imes V = 5 	imes 7 = 35 
eq 12$.Process $B$: $P 	imes V = 4 	imes 6 = 24 
eq 12$.Process $C$: $P 	imes V = 12 	imes 1 = 12$.Process $D$: $P 	imes V = 6 	imes 3 = 18 
eq 12$.Thus, only process $C$ satisfies the condition $P_f V_f = P_i V_i$.

$A$. Process $A$	$P=5, V=7$
$B$. Process $B$	$P=4, V=6$
$C$. Process $C$	$P=12, V=1$
$D$. Process $D$	$P=6, V=3$

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