Two samples A and B are initially kept in the same state. Sample … - Vidyadip

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
$p_A > p_B$
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 $f',$ respectively.
Let the final volumes of both be $V_o$.
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 $p-V$ diagram, $p_A < p_B.$

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