The given graph shows four different processes (adiabatic, isothermal, isobaric, and isochoric) for an ideal gas starting from the same initial state. Study the graph carefully and state which statement is correct:
Show Hint
Remember these simple geometric rules for $P-V$ plots: Vertical line = Isochoric (constant volume), Horizontal line = Isobaric (constant pressure). This allows you to identify Path 1 as isochoric and choose Option (C) right away.
Concept:
Thermodynamic state changes are plotted on a $P-V$ diagram (Pressure versus Volume) to illustrate work and energy tracking.
• Isobaric: Constant pressure ($\Delta P = 0$). This processes plots as a horizontal line.
• Isochoric: Constant volume ($\Delta V = 0$). This processes plots as a vertical line.
• Isothermal vs Adiabatic: Both show downward sloping curves. Because an adiabatic change involves no heat transfer, its slope is steeper by a factor of $\gamma$ compared to an isothermal path ($\text{Slope}_{\text{adiabatic}} = \gamma \cdot \text{Slope}_{\text{isothermal}}$).
Step 1: Identify each process line on the plot.
Matching the slopes from the common starting point:
• Path 1 is perfectly vertical, meaning volume is fixed. This is an isochoric process.
• Path 2 is the less steep curve, representing an isothermal process.
• Path 3 is the steeper curve, representing an adiabatic process.
• Path 4 is perfectly horizontal, meaning pressure is fixed. This is an isobaric process.
Comparing these definitions to the options, Statement (C) is correct.
