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(C) The equation of a polytropic process is $PV^x = 	ext{constant}$,which can be written as $\log P + x \log V = 	ext{constant}$,or $\log P = -x \lo

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$C_P > C_B > C_A > C_V$

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(C) The equation of a polytropic process is $PV^x = 	ext{constant}$,which can be written as $\log P + x \log V = 	ext{constant}$,or $\log P = -x \log V + 	ext{constant}$.Comparing this with the equation of a line $y = mx + c$,the slope $m = -x$.For process $A$,the slope is $	an(	heta_A) = \gamma$. Thus,$-x_A = \gamma$,so $x_A = -\gamma$.The molar heat capacity for a polytropic process is $C = C_V + \frac{R}{1-x}$.For process $A$,$C_A = C_V + \frac{R}{1 - (-\gamma)} = C_V + \frac{R}{1+\gamma}$. Since $\gamma > 1$,$C_A$ is a finite positive value.For process $B$,the slope is $	an(45^\circ) = 1$. Thus,$-x_B = 1$,so $x_B = -1$.For process $B$,$C_B = C_V + \frac{R}{1 - (-1)} = C_V + \frac{R}{2}$.Comparing the values:$C_P = C_V + R$$C_B = C_V + 0.5R$$C_A = C_V + \frac{R}{1+\gamma}$ (where $1 Thus,$C_P > C_B > C_A > C_V$.

Two thermodynamic processes are shown in the figure. The molar heat capacities for processes $A$ and $B$ are $C_A$ and $C_B$. The molar heat capacities at constant pressure and constant volume are represented by $C_P$ and $C_V$,respectively. Choose the correct statement.

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