However, calculating probabilities like W can be very challenging. Using statistical probability is very useful for visualizing how a process occurs. That is to say, doubling the number of molecules doubles the entropy. It is clear from this equation that entropy is an extensive property and depends on the number of molecules. The above equation is known as Boltzmann Equation, named after Austrian physicist Ludwig Boltzmann. W: Number of microstates corresponding to a given macrostate The key assumption made here is that each possible outcome is equally probable, leading to the following equation: Using Statistical Probability: Boltzmann Equation It can be quantitatively measured in terms of a system’s statistical probabilities or other thermodynamic quantities. How to Calculate EntropyĮntropy is a qualitative measure of how much the energy of atoms and molecules spreads during a process. These attributes of entropy are essential for formulating the Second Law of Thermodynamics. A positive entropy means an increase in disorder. Generally, the combined entropy of the system and the surrounding for a spontaneous process increases. Entropy and the Second Law of ThermodynamicsĪ system at equilibrium does not undergo an entropy change because no net change is occurring. Entropy is often called the arrow of time because matter tends to move from order to disorder in isolated systems. Since entropy measures disorder, a highly ordered system has low entropy, and a highly disordered one has high entropy. It is an extensive property, meaning entropy depends on the amount of matter. Entropy and the Second Law of ThermodynamicsĮntropy is a thermodynamic state function that measures the randomness or disorder of a system.The fact that a perfect crystal of a substance at 0 K has zero entropy is sometimes called the Third Law of Thermodynamics. This is because we know that the substance has zero entropy as a perfect crystal at 0 K there is no comparable zero for enthalpy. The reason is that the entropies listed are absolute, rather than relative to some arbitrary standard like enthalpy. Note that there are values listed for elements, unlike DH fº values for elements. The Thermodynamics Table lists the entropies of some substances at 25 ✬. Continue this process until you reach the temperature for which you want to know the entropy of a substance (25 ✬ is a common temperature for reporting the entropy of a substance). Then you can use equation (1) to calculate the entropy changes. Even though equation (1) only works when the temperature is constant, it is approximately correct when the temperature change is small. Now start introducing small amounts of heat and measuring the temperature change. Since there is no disorder in this state, the entropy can be defined as zero. Imagine cooling the substance to absolute zero and forming a perfect crystal (no holes, all the atoms in their exact place in the crystal lattice). The absolute entropy of any substance can be calculated using equation (1) in the following way. At absolute 0 (0 K), all atomic motion ceases and the disorder in a substance is zero. On this scale, zero is the theoretically lowest possible temperature that any substance can reach. The temperature in this equation must be measured on the absolute, or Kelvin temperature scale. Using this equation it is possible to measure entropy changes using a calorimeter. Where S represents entropy, DS represents the change in entropy, q represents heat transfer, and T is the temperature. One useful way of measuring entropy is by the following equation:
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