WEBVTT
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So, we looked at the 2nd laws.
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At first, it was on the conversion from heat to work or the amount of useful energy in isolated system.
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So, the 2nd law statements were all about entropy. Then, how are they related? What is entropy?
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The entropy is related with the useful energy.
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Entropy is the thermodynamic property that can be used to determine the energy
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not available for work in the process.
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In other words, it is the decrease in useful energy in the process.
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In statistical thermodynamics, the entropy is the number of microstates available,
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so it is equivalent to the degree of randomness or chaos.
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We are not going into the statistical thermodynamics in this course,
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but keep in mind that the decrease in useful energy is kind of increasing degree of randomness or chaos.
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Let's think about entropy as a thermodynamic function.
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Historically, people found that in a closed system,
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reversible heat divided by temperature is a point function,
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and define it as the entropy change of a system for a closed system.
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From the first law, dU is delta Q + delta W for the reversible process.
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Since internal energy U is a point function,
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it is also the same with delta Q + delta W for the actual process. Rearrange the equation.
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Delta Q reversible is thus equal to delta Q actual + delta W actual - delta W reversible.
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Combine the two works together and define it as the lost work lw.
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Then, delta Q reversible is delta Q actual + delta lost work.
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Inserting into the definition of entropy results in this equation.
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The entropy change of the close system is actual heat - lost work divided by temperature.
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Let's look at the concept of lost work in details.
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Consider that our ideal gas system expanses from state A to state B.
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The first process is the isothermal reversible expansion.
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The area under this P-V curve is the work done by the system.
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Then, let's consider another path. This path is, starting from the state A,
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first follow the constant volume process for pressure decrease from P1 to P2,
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then proceed to state B following constant pressure process.
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The area under this constant pressure line is the work done by this process.
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Here, we can see that the work done by the reversible process is larger
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and the difference is the lost work.
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So the entropy change of the system is Q actual - lost work divided by T.
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Here, we define irreversible entropy as - lost work divided by T
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Then, entropy of the system is actual heat divided by divided T + irreversible entropy.
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But we need a caution. This is for the the closed system.
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For surrounding, entropy is define by the actual heat, not the reversible heat divided by temperature.
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So the entropy of surrounding is not a point function.