In thermodynamics, entropy is a state function that measures disorder and energy unavailability. What is the SI unit of entropy?

Introduction / Context:
This question tests your knowledge of the correct SI unit for entropy, an important concept in thermodynamics. Entropy is associated with the degree of randomness or disorder in a system and with the amount of energy that is not available to do useful work. Understanding its unit is important when using thermodynamic equations such as those for reversible processes and for changes in entropy in heat transfer problems.

Given Data / Assumptions:

• We consider entropy as defined in classical thermodynamics.
• We work with the SI (International System of Units).
• Options given include watt per kelvin, newton per kelvin, pascal per kelvin and joule per kelvin.
• No advanced statistical mechanics framework is required, only the standard engineering definition.

Concept / Approach:
Entropy change dS for a reversible process is defined by the relation dS = dQ_rev / T, where dQ_rev is the reversible heat transfer and T is absolute temperature. In SI units, heat dQ_rev is measured in joule and temperature T is measured in kelvin. Therefore, entropy and entropy change have the unit joule per kelvin (J/K). The other units listed arise from force, power or pressure relationships and do not match this ratio of energy to temperature.

Step-by-Step Solution:
Step 1: Recall the thermodynamic definition for reversible processes: dS = dQ_rev / T. Step 2: Identify the units: dQ_rev is heat transfer measured in joule (J). Step 3: Temperature T is measured in kelvin (K) in the SI system. Step 4: So the unit of dS is (joule) / (kelvin) or J/K. Step 5: Recognise that this unit applies to entropy S itself and to its changes. Step 6: Compare with the given options and see that joule per kelvin is present as one of them. Step 7: Conclude that the correct SI unit of entropy is joule per kelvin.

Verification / Alternative check:
Textbooks on thermodynamics and engineering handbooks list entropy values such as specific entropy s in units of J/(kg K) and total entropy S in J/K. These consistent usages confirm that joule per kelvin is the accepted SI unit. Also, when applying the second law of thermodynamics to cycles or processes, entropy changes are always expressed with energy in the numerator and temperature in the denominator, reinforcing the J/K unit structure.

Why Other Options Are Wrong:
Watt per kelvin combines power (J/s) and temperature, and is used in some heat transfer coefficients, not as the unit of entropy itself. Newton per kelvin mixes force and temperature and has no standard role as a unit of entropy. Pascal per kelvin involves pressure per temperature and is not used for entropy; it belongs to different derived quantities.

Common Pitfalls:
Students sometimes confuse entropy units with those of related quantities like heat transfer coefficient or specific heat capacity. Specific heat capacity, for example, has units J/(kg K), which may appear similar but include mass in the denominator. Entropy per unit mass does share this same form, so it is important to distinguish between total entropy (J/K) and specific entropy (J/(kg K)). Focusing on the basic relation dS = dQ_rev / T helps fix the correct unit firmly in memory.

Final Answer:
The SI unit of entropy is joule per kelvin (J/K).