Question: 2: An ideal gas undergoes four different processes from the same initial state as shown in the figure below. Those processes are adiabatic, isothermal, isobaric and isochoric. The curve which represents the adiabatic process among 1,2,3 and 4 is
(1) 3
(2) 4
(3) 1
(4) 2
Answer: Option (4)
Explanation:
The given diagram is a pressure–volume P\text{-}V graph showing four different thermodynamic processes starting from the same initial state.
An isochoric process occurs at constant volume, so it is represented by a vertical line on a P\text{-}V graph. Hence, curve 1 is the isochoric process.
An isobaric process occurs at constant pressure, so it is represented by a horizontal line on a P\text{-}V graph. Hence, curve 4 is the isobaric process.
The remaining two curves, 2 and 3, represent isothermal and adiabatic processes. For an ideal gas,
the equations are PV = \text{constant} for isothermal and
PV^{\gamma} = \text{constant} for adiabatic processes,
where \gamma > 1.
Since pressure decreases more rapidly with increase in volume for an adiabatic process than
for an isothermal process, the adiabatic curve is steeper and lies below the isothermal curve.
In the diagram, curve 2 is steeper and lies below curve 3.
Therefore, curve 2 represents the adiabatic process.