Question

${}^{\prime }{n}^{\prime }$ moles of an ideal gas with molar mass $M$ undergoes a cyclic process as shown below in pressure vs density graph.

• A. $AB$ and $CD$ are isochoric whereas $BC$ and $DA$ are isothermal processes
• B. $AB$ and $CD$ are isothermal whereas $BC$ and $DA$ are isochoric processes
• C. Corresponding P-V diagram is
  
• D. Corresponding P-V diagram is
  

Answer 1

Answer: (A), (D)

The correct options are
A $AB$ and $CD$ are isochoric whereas $BC$ and $DA$ are isothermal processes
D Corresponding P-V diagram is


Density $\rho =\frac{nM}{V}$. Therefore $\rho \propto \frac{1}{V}$
During AB and CD, $\rho$ is constant, so $\frac{1}{V}$ is constant. Therefore, they are isochoric processess.
During BC and DA, $P\propto \rho \Rightarrow P\propto \frac{1}{V}$
Therefore, PV is constant. So, they are isothermal processess.
So options (1) and (4) are correct.