Entropy is a fundamental concept in thermodynamics that measures the randomness or disorder of a system. While it is often defined as a measure of disorder, a more precise understanding is that entropy quantifies the randomness of a system's energy distribution. For instance, consider two jars of colored balls: when they are mixed, the system becomes more randomized, resulting in higher entropy. Conversely, when the balls are separated, the system exhibits lower entropy due to less randomness.
In thermodynamics, entropy is crucial for understanding how energy is spread within a system. For example, comparing ice and water, one might assume ice is more disordered due to its solid state. However, at the atomic level, ice's atoms are fixed in place, leading to lower entropy. In contrast, water's molecules can move freely, allowing for greater energy distribution and thus higher entropy. Generally, systems at higher temperatures possess more energy, which contributes to increased randomness and higher entropy.
To calculate the change in entropy, denoted as ΔS, the relevant equation is:
\[\Delta S = \frac{q}{T}\]
Here, \(q\) represents the heat transferred, and \(T\) is the absolute temperature in Kelvin. This equation is applicable only for isothermal processes, where the temperature remains constant. It is important to note that the units for entropy change are joules per kelvin (J/K).
For example, if 24,100 joules of energy is added to a large body of water at a constant temperature of 27°C (which converts to 300 K), the change in entropy can be calculated as:
\[\Delta S = \frac{24100 \, \text{J}}{300 \, \text{K}} = 80.33 \, \text{J/K}\]
This indicates that the entropy of the water increases as energy is added, spreading the energy more evenly throughout the system.
Another scenario involves calculating the change in entropy when 2 kilograms of water freezes into ice. The heat transfer during this phase change can be calculated using the latent heat of fusion:
\[\Delta S = \frac{-mL_F}{T}\]
In this case, \(m\) is the mass of the water, \(L_F\) is the latent heat of fusion (approximately \(3.34 \times 10^5 \, \text{J/kg}\)), and \(T\) is the freezing temperature in Kelvin (273 K). Plugging in the values:
\[\Delta S = \frac{-2 \times 3.34 \times 10^5 \, \text{J/kg}}{273 \, \text{K}} \approx -2447 \, \text{J/K}\]
This negative value indicates that the entropy decreases when heat is removed during the freezing process. In summary, the sign of ΔS corresponds to the direction of heat transfer: adding heat results in positive entropy change, while removing heat leads to negative entropy change.
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