Entropy

So, we looked at the 2nd laws. At first, it was on the conversion from heat to work or the amount of useful energy in isolated system. So, the 2nd law statements were all about entropy. Then, how are they related? What is entropy? The entropy is related with the useful energy. Entropy is the thermodynamic property that can be used to determine the energy not available for work in the process. In other words, it is the decrease in useful energy in the process. In statistical thermodynamics, the entropy is the number of microstates available, so it is equivalent to the degree of randomness or chaos.

We are not going into the statistical thermodynamics in this course, but keep in mind that the decrease in useful energy is kind of increasing degree of randomness or chaos. Let’s think about entropy as a thermodynamic function. Historically, people found that in a closed system, reversible heat divided by temperature is a point function, and define it as the entropy change of a system for a closed system. From the first law, dU is delta Q + delta W for the reversible process. Since internal energy U is a point function, it is also the same with delta Q + delta W for the actual process. Rearrange the equation.

Delta Q reversible is thus equal to delta Q actual + delta W actual - delta W reversible. Combine the two works together and define it as the lost work lw. Then, delta Q reversible is delta Q actual + delta lost work. Inserting into the definition of entropy results in this equation. The entropy change of the close system is actual heat - lost work divided by temperature. Let’s look at the concept of lost work in details. Consider that our ideal gas system expanses from state A to state B. The first process is the isothermal reversible expansion. The area under this P-V curve is the work done by the system. Then, let’s consider another path.

This path is, starting from the state A, first follow the constant volume process for pressure decrease from P1 to P2, then proceed to state B following constant pressure process. The area under this constant pressure line is the work done by this process. Here, we can see that the work done by the reversible process is larger and the difference is the lost work. So the entropy change of the system is Q actual - lost work divided by T. Here, we define irreversible entropy as - lost work divided by T Then, entropy of the system is actual heat divided by divided T + irreversible entropy. But we need a caution. This is for the the closed system.

For surrounding, entropy is define by the actual heat, not the reversible heat divided by temperature. So the entropy of surrounding is not a point function.