Question

Which of the following equations does not state a law of thermodynamics? A. \(\Delta E_{\text {syskm }}+\Delta E_{\text {surroundings }}=\Delta E_{\text {universe }}\) B. \(\Delta S_{\text {systam }}+\Delta S_{\text {surroundings }}=\Delta S_{\text {universe }}\) C. \(\Delta H_{\text {syskem }}+\Delta H_{\text {sarroundings }}=\Delta H_{\text {univarse }}\) D. \(S_{\text {universe }}=0\) at \(T=0 \mathrm{~K}\).

Short answer

Option C does not state a law of thermodynamics.

Step-by-step solution

- Understanding Thermodynamic Laws

Review the laws of thermodynamics. The first law (conservation of energy) can be written as \(\Delta E_{\text {system }}+\Delta E_{\text {surroundings }}=\Delta E_{\text {universe }}\). The second law involves entropy changes, written as \(\Delta S_{\text {system }}+\Delta S_{\text {surroundings }}=\Delta S_{\text {universe }}\). The third law states that the entropy of a perfect crystal at absolute zero is zero, hence \(S_{\text {universe }}=0\) at \( T=0 \,\text{K}\).

- Identifying Errors

Examine the equations given in the question. Check if they match the thermodynamic laws identically or contain errors/typos. Equations A, B, and D match known thermodynamic laws.

- Analyzing Option C

Observe equation C: \(\Delta H_{\text {system }}+\Delta H_{\text {surroundings }}=\Delta H_{\text {universe }}\). The term \(\Delta H\) represents enthalpy. The laws of thermodynamics do not sum enthalpies of the system and surroundings to the universe. Thus, this does not state a thermodynamic law.

Key concepts

Conservation of Energy

Conservation of energy is the backbone of the first law of thermodynamics. This law tells us that energy cannot be created or destroyed but can only change forms. Think of it like a pie: no matter how you slice it, the total amount remains constant. In thermodynamic terms, it is represented as \(\backslash\Delta E_{\text {system }}+\backslash\Delta E_{\text {surroundings }}=\backslash\Delta E_{\text {universe }}\).

• \( \backslash\Delta E_{\text {system }} \) - Energy change within the system
• \( \backslash\Delta E_{\text {surroundings }} \) - Energy change in the surroundings
• \( \backslash\Delta E_{\text {universe }} \) - Total energy change in the universe

This principle is fundamental in all energy exchanges. For instance, when you rub your hands together, mechanical energy turns into heat energy, but the total energy remains unchanged.

Entropy

Entropy is a measure of disorder or randomness in a system. It is closely tied to the second law of thermodynamics, which states that the total entropy of an isolated system will never decrease over time. Mathematically, it’s expressed as \( \backslash\Delta S_{\text {system }}+\backlash\Delta S_{\text {surroundings }}=\backslash\Delta S_{\text {universe }} \).

• \( \backslash\Delta S_{\text {system }} \) - Entropy change within the system
• \( \backslash\Delta S_{\text {surroundings }} \) - Entropy change in the surroundings
• \( \backslash\Delta S_{\text {universe }} \) - Total entropy change in the universe

Entropy helps explain why some processes are irreversible; they contribute to an increase in universal entropy. When you melt an ice cube, the orderly structure of ice changes to the more disordered structure of water, increasing the system's entropy.

Enthalpy

Enthalpy (\(\backslash\Delta H \)) is the total heat content of a system. It's important in describing how heat flows during reactions at constant pressure. However, it's crucial to know that the laws of thermodynamics do not state that the sum of enthalpies of the system and surroundings equals the universe, unlike energy and entropy.

Instead, enthalpy changes focus on heat transfer during chemical reactions:

• For exothermic reactions, \(\backslash\Delta H \backslash\lt 0\) - heat is released.
• For endothermic reactions, \(\backlash\Delta H \backslash\gt 0\) - heat is absorbed.

Think of enthalpy as a measure of the heat energy in a given system. During a chemical reaction, measuring \(\backslash\Delta H \) lets us understand if the reaction system gains or loses heat.

Absolute Zero Entropy

The concept of absolute zero entropy is part of the third law of thermodynamics. It states that as a system approaches absolute zero temperature (\(T=0 \text{K}\)), the entropy of a perfect crystal approaches zero. At this point, the atoms are in a state of minimum energy with maximum order, thus zero entropy.

This can be expressed as \(S_{\text {system }} = 0 \text{ at } T = 0 \text{K}\).

• \( \text{K} \) - Kelvin, the unit of absolute temperature.
• \(\text{Perfect crystal}\) - A theoretical material with no imperfections or disorder.

This principle has practical implications, such as in cryogenics and understanding low-temperature behaviors of materials. However, reaching absolute zero is theoretically impossible. It remains a guiding principle that helps us understand low-temperature thermodynamics.