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JEE Advanced 2022 Paper 1 · Physics · Thermodynamics and Kinetic Theory of Gases · medium

One mole of a monatomic ideal gas at pressure P0, volume V0 and temperature T0 expands reversibly and adiabatically to a volume 8V0.

One or more options correct

One mole of a monatomic ideal gas at pressure P0P_0, volume V0V_0 and temperature T0T_0 expands reversibly and adiabatically to a volume 8V08V_0. Choose the correct option(s).
  1. A. The final pressure is P0/16P_0/16.
  2. B. The work done by the gas is 98P0V0\tfrac98P_0V_0.
  3. C. The final temperature is T0/2T_0/2.
  4. D. The entropy of the gas increases.
Show answer and solution

Answer: B

For γ=5/3\gamma=5/3, PVγ=constPV^\gamma=\text{const} gives Pf=P0 8−5/3=P0/32P_f=P_0\,8^{-5/3}=P_0/32, so (A) is false. TVγ−1=constTV^{\gamma-1}=\text{const} gives Tf=T0 8−2/3=T0/4T_f=T_0\,8^{-2/3}=T_0/4, so (C) is false. Work =Cv(T0−Tf)=32RT0×34=98P0V0=C_v(T_0-T_f)=\tfrac32RT_0\times\tfrac34=\tfrac98P_0V_0, so (B) is true. A reversible adiabatic process is isentropic (dS=δQ/T=0dS=\delta Q/T=0), so (D) is false.
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