Key Thermodynamic Processes

Why This Matters

Thermodynamics is where energy conservation meets real-world applications—and the AP Physics 2 exam loves testing whether you understand how and why energy moves through systems. You're not just being tested on definitions; you're being tested on your ability to analyze PV diagrams, apply the first law ($\Delta U = Q + W$), and predict what happens to temperature, pressure, and volume when one variable is held constant. These processes form the foundation for understanding heat engines, refrigerators, and entropy—all fair game for both multiple choice and FRQs.

The key insight is that each thermodynamic process represents a constraint on the system: hold temperature constant, hold pressure constant, block heat transfer, or keep volume fixed. Each constraint produces different relationships between heat, work, and internal energy. Don't just memorize that "isothermal means constant temperature"—know that constant temperature means $\Delta U = 0$ for an ideal gas, which forces $Q = W$. That's the level of reasoning that earns you points.

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Constant-Variable Processes

These processes define what stays fixed while the system changes. The constraint you impose determines how energy flows between heat and work.

Isothermal Process

• Temperature stays constant, so for an ideal gas, internal energy doesn't change ($\Delta U = 0$)
• Heat equals work ($Q = W$)—any energy entering as heat leaves as work done by the system
• PV diagram shows a hyperbola—the curve follows $PV = nRT = \text{constant}$

Isobaric Process

• Pressure remains constant while volume and temperature change together
• Work is straightforward: $W = -P\Delta V$, making this the easiest process for calculating work graphically
• Heat changes both internal energy and does work—you need $C_p$ (molar heat capacity at constant pressure) for calculations

Isochoric Process

• Volume is fixed, meaning the gas can't expand or compress, so $W = 0$
• All heat becomes internal energy: $\Delta U = Q$, the simplest application of the first law
• PV diagram shows a vertical line—pressure changes while volume stays put

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Heat-Blocked Processes

When a system can't exchange heat with its surroundings, all energy changes come from work alone. These processes are critical for understanding engine efficiency.

Adiabatic Process

• No heat transfer ($Q = 0$), so the first law simplifies to $\Delta U = W$
• Temperature changes as work is done—compression heats the gas, expansion cools it
• Follows $PV^\gamma = \text{constant}$, where $\gamma = C_p/C_v$ is the heat capacity ratio

Isentropic Process

• Reversible adiabatic process where entropy stays constant—the idealized version of adiabatic
• No heat exchange and no entropy generation—represents the theoretical limit of efficiency
• Used in idealized models of turbines and compressors where you assume no friction or irreversibility

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Cyclic and Multi-Step Processes

Real applications involve sequences of processes that return the system to its starting point. The power of cycles is that internal energy resets, so net work equals net heat.

Cyclic Process

• System returns to initial state, so $\Delta U_{\text{cycle}} = 0$
• Net work equals net heat: $W_{\text{net}} = Q_{\text{net}}$—the area enclosed by the cycle on a PV diagram
• Clockwise cycles do positive work (engines); counterclockwise cycles require work input (refrigerators)

Heat Engines and the Carnot Cycle

• Heat engines convert thermal energy to mechanical work by operating between hot and cold reservoirs
• Carnot efficiency sets the maximum: $\eta = 1 - \frac{T_c}{T_h}$, using absolute temperatures in Kelvin
• No real engine beats Carnot—this limit comes directly from the second law of thermodynamics

Refrigeration Cycles

• Move heat from cold to hot, which requires work input—heat doesn't flow uphill spontaneously
• Coefficient of performance (COP) measures effectiveness: higher COP means more cooling per unit work
• Reverse Carnot cycle represents the theoretical maximum COP for refrigeration

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Generalized and Real-World Processes

These processes describe behavior that doesn't fit neatly into the idealized categories. Real gases and engineering applications often require more flexible models.

Polytropic Process

• Follows $PV^n = \text{constant}$, where $n$ is the polytropic index
• Bridges all other processes: $n = 0$ (isobaric), $n = 1$ (isothermal), $n = \gamma$ (adiabatic), $n = \infty$ (isochoric)
• Models real gas behavior when processes don't perfectly match idealized assumptions

Throttling Process

• Pressure drops without heat exchange—fluid passes through a valve or constriction
• Joule-Thomson effect causes temperature to drop for most gases at typical conditions
• Essential for refrigeration—this is how your refrigerator actually achieves cooling

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Quick Reference Table

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Self-Check Questions

1. For an ideal gas undergoing an isothermal expansion, why does $Q = W$? What does this tell you about the relationship between heat input and work output?

2. Compare isochoric and adiabatic processes: which one has $\Delta U = Q$, and which has $\Delta U = W$? Explain why each relationship follows from the first law.

3. On a PV diagram, you see a closed loop traced clockwise. What can you immediately conclude about the net work and whether this represents a heat engine or refrigerator?

4. Why can no real heat engine exceed Carnot efficiency? Connect your answer to the second law of thermodynamics and entropy.

5. A gas undergoes throttling through a valve. Explain why this process is irreversible even though $Q = 0$, and describe what happens to the entropy of the system.