One mole of an ideal gas goes from an initial state $A$ to the final state $B$ with two processes. It first un

Question

One mole of an ideal gas goes from an initial state $A$ to the final state $B$ with two processes. It first undergoes isothermal expansion from volume $V$ to $3V$ and then its volume is reduced from $3V$ to $V$ at constant pressure. The correct $(P-V)$ diagram representing the two processes is:

Accepted Answer

The thermodynamic path consists of two distinct processes:

1.  **Isothermal Expansion:** The gas expands from volume $V$ to $3V$ at constant temperature ($T$). For an ideal gas, $PV = nRT$ . Since $T$ is constant, $P \propto 1/V$ (Boyle's Law). On a $P-V$ diagram, this is represented by a hyperbolic curve sloping downwards from initial volume $V$ to $3V$ .

2.  **Isobaric Compression:** The gas is compressed from volume $3V$ back to $V$ at constant pressure. This is represented by a straight horizontal line moving from right ($3V$) to left ($V$) .

Thus, the correct graph traces a curve downwards to the right, followed by a horizontal line to the left.

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