MCQ
Two samples $A$ and $B$ are initially kept in the same state. Sample $A$ is expanded through an adiabatic process and the sample $B$ through an isothermal process. The final volumes of the samples are the same. The final pressures in $A$ and $B$ are $p_A$ and $p_B$ respectively.
  • A
    $\mathrm{p}_{\mathrm{A}} > \mathrm{p}_{\mathrm{B}}$
  • B
    $p_A=p_B$
  • $p_A < p_B$
  • D
    The relation between $p_A$ and $p_B$ cannot be deduced.

Answer

Correct option: C.
$p_A < p_B$

Let the initial states of samples $A$ and $B$ be i and the final states of samples $B$ and $A$ be $f$ and $f^{\prime}$, respectively.
Let the final volumes of both be $V_0$. As sample $A$ is expanded through an adiabatic process, its curve in the $p-V$ diagram is steeper than that of sample $B ,$ which is expanded through an isothermal process.
Therefore, from the $\mathrm{p}-\mathrm{V}$ diagram, $\mathrm{p}_{\mathrm{A}}\ <\  \mathrm{p}_{\mathrm{B}}$.

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