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For an adiabatic expansion of an ideal gas, the fractional change in its pressure is equal to (where γ is the ratio of specific heats)

Asked in JEE Main 18th March 2nd Shift 2021 · Ratio of specific heats

• (1) - γ V/(dV)
• (2) - 1/γ (dV)/V
• (3) - γ (dV)/V
• (4) (dV)/V

Step-by-step solution

Why the other options are wrong

• (1) Inverts the volume differential; (dV)/V is the fractional change, not V/(dV).
• (2) Puts γ in the denominator; differentiating γ ln V brings γ out as a multiplier.
• (4) Loses both γ and the minus sign, so an expansion would raise the pressure.

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