Question

5 moles of an ideal monatomic gas undergoes adiabatic free expansion from $10L$, $\left(e^4\right)$ atm to (e) atm. The change in entropy (in Cal/K) of the system is:
[Answer as xyz, in which x = 1 if $\Delta S=$ +ve and x = 0 if $\Delta S=$ -ve and yz are representing the numerical value of $\Delta S$

Answer 1

Since the process is performed under free expansion, $w=0$ and $\Delta U=0$ then it is also isothermal process. Hence,
$\Delta S=nRln\frac{P_1}{P_2}$
$\Delta S=30$
$P_1=e^4$
$P_2=e^1$

$\Delta S=5\times Rln\frac{e^4}{e^1}$
$=5\times R[ln{e}^4-ln{e}^1]$
$=5\times R\times [4-1]$
$=5\times 2\times 3=30$ cal
$\Delta S=$ +ve
$x=1$
y z
3 0

x y z
1 3 0