Question

Initially two gas samples $1$ and $2$ are at the same condition. The volume of the two are halved, one isothermally and the other adiabatically. What is the relation between the final pressure $P_1$ and $P_2$ ?

• A. $P_1 = P_2$
• B. $P_1 > P_2$
• C. $P_2 > P_1$
• D. Cannot be determined

Answer 1

Answer: (C)

$P_2 > P_1$

Answer 2

For isothermal process
$PV = K$ (constant)
$P =\frac{ K }{ V } \ldots(1)$
$=\frac{ K }{ V / 2}=2 K$
For adiabatic process
$PV ^{\gamma}= K$ (constant)
$\therefore P =\frac{ K }{ V ^{\gamma}} \ldots . .(2)$
$=\frac{ K }{( V / 2)^{\gamma}}- K \left(2^{\gamma}\right)$
From Eqs. (1) and (2), we have
$P _{2} > P _{1}$