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Entropy - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

Quick Facts

  • Entropy is considered one of the most asked concept.

  • 8 Questions around this concept.

Solve by difficulty

Which of the following is incorrect regarding the first law of thermodynamics?

The temperature­- entropy diagram of a reversible engine cycle is given in the figure. Its efficiency is

Concepts Covered - 1

Entropy

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 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 

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   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 ideal gas in terms of T & V

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

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

using PV = nRT  

\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 )+nR\ln \left ( \frac{V_{2}}{V_{1}} \right )

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 )-nR\ln \left ( \frac{P_{2}}{P_{1}} \right )

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

\Delta S= nC_{V}\ln \left ( \frac{P_{2}}{P_{1}} \right )+n\, C_{P}\ln \left ( \frac{V_{2}}{V_{1}} \right )

 

 

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Entropy

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