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NEET PHYSICSThermodynamicsMedium

Question

An ideal gas is compressed to half its initial volume using several processes. Which of the processes results in the maximum work done on the gas?

A

adiabatic

B

isobaric

C

isochoric

D

isothermal

Step-by-Step Solution

The work done on a gas during compression is given by the area under the pressure-volume (PVP-V) curve (w=PexdVw = -\int P_{ex} dV) .

  1. Isochoric Process: The volume is constant (dV=0dV = 0), so the work done is zero .
  2. Isobaric Process: The pressure is constant. The work done is the area of the rectangle under the horizontal line.
  3. Isothermal vs. Adiabatic: For an ideal gas, the slope of the adiabatic curve (PVγ=constantPV^\gamma = \text{constant}) is steeper than that of the isothermal curve (PV=constantPV = \text{constant}) because γ>1\gamma > 1. During compression from an initial volume VV to V/2V/2, the final pressure attained in an adiabatic process is higher than in an isothermal process (since temperature increases in adiabatic compression but remains constant in isothermal).
  • Consequently, the P-V curve for adiabatic compression lies above the isothermal curve, enclosing a larger area.

Therefore, the maximum work is done in the adiabatic compression.

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from Thermodynamics. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSThermodynamicscompressedinitialvolumeseveralprocesses

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