Change in entropy in reversible carnot's cycle (most important for BSc 1st year))

 Here is the derivation of change in entropy in reversible Carnot's cycle 

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Consider ABCDA be reversible Carnot's cycle in this cycle, AB be isothermal expansion. BC be the adiabatic expansion CD be the Isothermal comparison and DA be the adiabatic compression.

During Isothermal Expansion from A to B, the working substance absorbed amount of heat Q1 from source at temp. T1. Hence gain in entropy of working substance from A to B is Q1/T1 ( source lose heat Q1 and T1, so its entropy decreased by Q1/T1).

During Adiabatic Expansion from B to C, there is no change in entropy, (since no exchange heat between system and surrounding).

During Isothermal compression from C to D, the working substance reject amount of heat Q2 to sink at temperature T2.

Hence, loss in entropy of working substance from C to D is Q2/T2. {since sink gain heat Q2. So, its entropy is increased by Q2/T2}

Similarly, During adiabatic compression from D to A, there is no change in entropy. Since no exchange heat between system and surrounding.

Total gain in entropy of working substance in whole carnot's cycle ABCDA = Q1/T1 - Q2/T2.

But, Q1/T1 = Q2/T2 { from carnot's theory }

Q1/T1-Q2/T2 = 0.

Thus total change in entropy of working substance is zero at complete cycle.

#physic 

#Bsc 1st year 

Heat and thermodynamic 

Carnot engiene