## Changes in Energy

#### Learning Objective

• Discuss the concept of entropy.

#### Key Points

• Increases in entropy correspond to irreversible changes in a system, because some energy is expended as heat, limiting the amount of work a system can do.
• Any process where the system gives up energy ΔE, and its entropy falls by ΔS, a quantity at least TR (temperature of the surroundings) multiplied by [latex]\Delta S[/latex] of that energy must be given up to the system’s surroundings as unusable heat.
• The dispersal of energy from warmer to cooler always results in a net increase in entropy.

#### Term

• quantizedExpressed or existing only in terms of discrete quanta; limited by the restrictions of quantization.

## Entropy

The concept of entropy evolved in order to explain why some processes (permitted by conservation laws) occur spontaneously while their time reversals (also permitted by conservation laws) do not; systems tend to progress in the direction of increasing entropy. For isolated systems, entropy never decreases. This fact has several important consequences in science: first, it prohibits “perpetual motion” machines; and second, it implies the arrow of entropy has the same direction as the arrow of time. Increases in entropy correspond to irreversible changes in a system. This is because some energy is expended as heat, limiting the amount of work a system can do.

In classical thermodynamics the entropy is interpreted as a state function of a thermodynamic system. A state function is a property depending only on the current state of the system, independent of how that state came to be achieved. The state function has the important property that in any process where the system gives up energy ΔE, and its entropy falls by ΔS, a quantity at least TR ΔS of that energy must be given up to the system’s surroundings as unusable heat (TR is the temperature of the system’s external surroundings). Otherwise the process will not go forward. The entropy of a system is defined only if it is in thermodynamic equilibrium. In a thermodynamic system, pressure, density, and temperature tend to become uniform over time because this equilibrium state has a higher probability (more possible combinations of microstates) than any other.

## Ice Water and Entropy

For example, consider ice water in a glass. The difference in temperature between a warm room (the surroundings) and a cold glass of ice and water (the system and not part of the room) begins to equalize. This is because the thermal energy from the warm surroundings spreads to the cooler system of ice and water. Over time, the temperature of the glass and its contents and the temperature of the room become equal. The entropy of the room decreases as some of its energy is dispersed to the ice and water. However, the entropy of the system of ice and water has increased more than the entropy of the surrounding room has decreased. Example of increasing entropyIce melting in a warm room is a common example of increasing entropy.

In an isolated system such as the room and ice water taken together, the dispersal of energy from warmer to cooler always results in a net increase in entropy. Thus, when the “universe” of the room and ice water system has reached a temperature equilibrium, the entropy change from the initial state is at a maximum. The entropy of the thermodynamic system is a measure of how far the equalization has progressed.

The second law of thermodynamics shows that in an isolated system internal portions at different temperatures will tend to adjust to a single uniform temperature and thus produce equilibrium. A recently developed educational approach avoids ambiguous terms and describes such spreading out of energy as dispersal. Physical chemist Peter Atkins, for example, who previously wrote of dispersal leading to a disordered state, now writes that “spontaneous changes are always accompanied by a dispersal of energy”.