Entropy - Practice Questions & MCQ

Entropy- Entropy is a measure of the disorder of the molecular motion of a system. I.e Greater is the disorder, greater is the entropy.

The change in entropy is given as

$
d S=\frac{\text { Heat absorbed by system }}{\text { Absolute temperature }} \text { or } d S=\frac{d Q}{T}
$

The relation

$
d S=\frac{d Q}{T}
$

1. Entropy for solid and liquid-
i. When heat is given to a substance to change its state at a constant temperature.

Then change in entropy is given as

$
d S=\frac{d Q}{T}= \pm \frac{m L}{T}
$

where positive sign refers to heat absorption and negative sign to heat evolution.
And $L=$ Latent Heat and T is in kelvin.
ii. When heat is given to a substance to raises its temperature from $T_1$ to $T_2$

Then change in entropy is given as

$
d S=\int \frac{d Q}{T}=\int_{T_1}^{T_2} m c \frac{d T}{T}=m c \log _e\left(\frac{T_2}{T_1}\right)=2.303 * \mathrm{mc}^{-\log _{10}}\left(\frac{T_2}{T_1}\right)
$

where $\mathrm{c}=$ specific heat capacity
2. Entropy for an ideal gas -

For $n$ mole of an ideal gas, the equation is given as $P V=n R T$
I.Entropy change for ideal gas in terms of T \& V

From the first law of thermodynamics, we know that $d Q=d W+d U$

$
\text { and } \Delta S=\int \frac{d Q}{T}=\int \frac{n C_V d T+P d V}{T}
$
 

using $\mathrm{PV}=\mathrm{nRT}$

$
\begin{aligned}
& \Delta S=\int \frac{n C_V d T+\frac{n R T}{V} d V}{T}=n C_V \int_{T_1}^{T_2} \frac{d T}{T}+n R \int_{V_1}^{V_2} \frac{d V}{V} \\
& \Delta S=n C_V \ln \left(\frac{T_2}{T_1}\right)+n R \ln \left(\frac{V_2}{V_1}\right)
\end{aligned}
$

II.Entropy change for an ideal gas in terms of T \& P

$
\Delta S=n C_P \ln \left(\frac{T_2}{T_1}\right)-n R \ln \left(\frac{P_2}{P_1}\right)
$

III.Entropy change for an ideal gas in terms of $\mathrm{P} \& \mathrm{~V}$

$
\Delta S=n C_V \ln \left(\frac{P_2}{P_1}\right)+n C_P \ln \left(\frac{V_2}{V_1}\right)
$