Second Law of Thermodynamics — Revision Notes

⚡ 30-Second Revision

Kelvin-Planck Statement: — No heat engine can be 100% efficient. $eta < 1$.
Clausius Statement: — Heat cannot spontaneously flow from cold to hot.
Carnot Efficiency: — $eta_{Carnot} = 1 - \frac{T_C}{T_H}$ (Temperatures in Kelvin).
Refrigerator COP: — $K_{refrigerator} = \frac{Q_C}{W} = \frac{T_C}{T_H - T_C}$.
Heat Pump COP: — $K_{heat,pump} = \frac{Q_H}{W} = \frac{T_H}{T_H - T_C}$.
Entropy Change (reversible): — $\Delta S = \frac{Q_{rev}}{T}$.
Principle of Increase of Entropy: — $\Delta S_{universe} \ge 0$ ($\Delta S_{universe} = 0$ for reversible, $>0$ for irreversible).
Work done by engine: — $W = Q_H - Q_C$.
Work done on refrigerator/heat pump: — $W = Q_H - Q_C$.

2-Minute Revision

The Second Law of Thermodynamics defines the direction of natural processes and limits energy conversion. The Kelvin-Planck statement asserts that no heat engine can convert all absorbed heat into work, implying efficiency is always less than 100%.

The Clausius statement says heat cannot spontaneously flow from a colder to a hotter body without external work. These statements are equivalent. The Carnot cycle represents the most efficient theoretical heat engine, with efficiency $eta = 1 - T_C/T_H$, where $T_C$ and $T_H$ are absolute temperatures of the cold and hot reservoirs.

Real engines are always less efficient. Refrigerators and heat pumps, which move heat against its natural gradient, require work input, and their performance is measured by the Coefficient of Performance (COP).

For a refrigerator, $K = T_C/(T_H-T_C)$, and for a heat pump, $K' = T_H/(T_H-T_C)$. Entropy ($S$) is a measure of disorder. The total entropy of an isolated system (or the universe) never decreases; it increases for irreversible processes and remains constant for reversible ones ($Delta S_{universe} ge 0$).

Remember to always use Kelvin for temperature in all formulas.

5-Minute Revision

The Second Law of Thermodynamics is crucial for understanding why processes occur in a specific direction and the fundamental limits on converting heat into work. It's articulated through two key statements: the Kelvin-Planck statement, which states that no heat engine can achieve 100% efficiency, meaning some heat must always be rejected to a colder reservoir; and the Clausius statement, which says heat cannot spontaneously flow from a colder to a hotter body without external work.

These are equivalent. The Carnot cycle is an ideal, reversible cycle that sets the maximum possible efficiency for any heat engine operating between two temperatures, given by $eta_{Carnot} = 1 - T_C/T_H$.

Always convert temperatures to Kelvin ($T_K = T_C + 273.15$). For example, if $T_H = 500,\text{K}$ and $T_C = 300,\text{K}$, $eta = 1 - 300/500 = 0.4$ or $40$. Real engines are always less efficient than Carnot engines.

Refrigerators and heat pumps are devices that transfer heat from cold to hot, requiring work input. Their effectiveness is measured by the Coefficient of Performance (COP). For a refrigerator, $K = Q_C/W = T_C/(T_H-T_C)$.

For a heat pump, $K' = Q_H/W = T_H/(T_H-T_C)$. Note that $K' = K+1$. For instance, a refrigerator operating between $273,\text{K}$ and $303,\text{K}$ has $K = 273/(303-273) = 273/30 = 9.1$. The concept of **entropy ($S$)**, a measure of disorder, is central.

For a reversible process, $Delta S = Q_{rev}/T$. The Principle of Increase of Entropy states that for an isolated system (or the universe), $Delta S_{universe} ge 0$. It is zero for reversible processes and positive for irreversible (real) processes.

This means natural processes tend towards greater disorder. Understanding these formulas and conceptual underpinnings is vital for NEET success.

Prelims Revision Notes

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Second Law Statements:

* Kelvin-Planck: No heat engine can have 100% efficiency. It must reject some heat to a cold reservoir. Implies $eta < 1$. * Clausius: Heat cannot spontaneously flow from cold to hot. Requires external work for such transfer. * Equivalence: Violation of one implies violation of the other.

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Heat Engines:

* Convert heat ($Q_H$) from a hot reservoir ($T_H$) into work ($W$), rejecting heat ($Q_C$) to a cold reservoir ($T_C$). * Work done: $W = Q_H - Q_C$. * Efficiency: $eta = \frac{W}{Q_H} = 1 - \frac{Q_C}{Q_H}$.

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Carnot Engine (Ideal Heat Engine):

* Most efficient theoretical engine operating between two temperatures. * Efficiency: $eta_{Carnot} = 1 - \frac{T_C}{T_H}$. Always use Kelvin temperatures! ($T_K = T_C + 273.15$). * Carnot's Theorem: No engine can be more efficient than a Carnot engine between the same temperatures. All reversible engines have the same efficiency.

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Refrigerators and Heat Pumps:

* Refrigerator: Transfers heat ($Q_C$) from cold ($T_C$) to hot ($T_H$) with work input ($W$). $Q_H = Q_C + W$. * Coefficient of Performance (COP): $K_{refrigerator} = \frac{Q_C}{W} = \frac{T_C}{T_H - T_C}$. * Heat Pump: Transfers heat ($Q_H$) to hot ($T_H$) from cold ($T_C$) with work input ($W$). $Q_H = Q_C + W$. * COP: $K_{heat,pump} = \frac{Q_H}{W} = \frac{T_H}{T_H - T_C}$. * Relationship: $K_{heat,pump} = K_{refrigerator} + 1$.

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**Entropy ($S$):**

* State function, measure of disorder/randomness. * Change in entropy for a reversible process: $\Delta S = \int \frac{\delta Q_{rev}}{T}$. For isothermal, $\Delta S = \frac{Q_{rev}}{T}$. * Unit: J/K.

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Principle of Increase of Entropy:

* For an isolated system (or the universe): $\Delta S_{universe} \ge 0$. * Reversible processes: $\Delta S_{universe} = 0$. * Irreversible (real) processes: $\Delta S_{universe} > 0$. * Entropy of a system can decrease, but only if the entropy of the surroundings increases by a greater amount, ensuring $\Delta S_{universe} \ge 0$.

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Reversible vs. Irreversible Processes:

* Reversible: Ideal, quasi-static, no dissipation, $\Delta S_{universe} = 0$. * Irreversible: Real, finite speed, dissipative effects (friction, heat transfer across finite $\Delta T$), $\Delta S_{universe} > 0$. All natural processes are irreversible.

Vyyuha Quick Recall

Cold Hot Efficiency: Carnot $\eta = 1 - T_C/T_H$. COP for Refrigerator: $K_R = T_C/(T_H-T_C)$. COP for Heat Pump: $K_{HP} = T_H/(T_H-T_C)$. Remember Kelvin for Temperatures!