Entropy MCQ - Practice Questions with Answers

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

The change in entropy is given as

$$dS=\frac{\text{ Heat absorbed by system }}{\text{ Absolute temperatu re }}\text{ or }dS=\frac{dQ}{T}$$

The relation $dS=\frac{dQ}{T}$ is called the mathematical form of the Second Law of Thermodynamics.
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

$$dS=\frac{dQ}{T}=\pm \frac{mL}{T}$$

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

Then change in entropy is given as

$$dS=\int \frac{dQ}{T}={\int }_{T_1}^{T_2}mc\frac{dT}{T}=mc{\log }_e\left(\frac{T_2}{T_1}\right)=2.303\ast {\mathrm{mc}}^{\log }{\log }_{10}\left(\frac{T_2}{T_1}\right)$$

where   c = specific heat capacity 

2. Entropy for an ideal gas  -

For n mole of an ideal gas, the equation is given as PV = nRT

I.Entropy change for an ideal gas in terms of T & V

From the first law of thermodynamics, we know that $dQ=dW+dU$

$$\mathrm{\Delta }S=\int \frac{dQ}{T}=\int \frac{n{C}_{V}dT+PdV}{T}$$

using $\mathrm{PV}=\mathrm{nR}T$

$$\begin{array}{rl}& \mathrm{\Delta }S=\int \frac{n{C}_{V}dT+\frac{nRT}{V}dV}{T}=n{C}_V{\int }_{T_1}^{T_2}\frac{dT}{T}+nR{\int }_{V_1}^{V_2}\frac{dV}{V}\\ & \mathrm{\Delta }S=n{C}_V\ln \left(\frac{T_2}{T_1}\right)+nR\ln \left(\frac{V_2}{V_1}\right)\end{array}$$

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

$$\mathrm{\Delta }S=n{C}_P\ln \left(\frac{T_2}{T_1}\right)-nR\ln \left(\frac{P_2}{P_1}\right)$$

III.Entropy change for an ideal gas in terms of P \& V

$$\mathrm{\Delta }S=n{C}_V\ln \left(\frac{P_2}{P_1}\right)+n{C}_P\ln \left(\frac{V_2}{V_1}\right)$$