🚀 What Are Thermodynamic State Variables?
Every equilibrium state of a system is pinned down by a set of big-picture numbers called state variables. For a gas the key ones are pressure (P), volume (V), temperature (T), and the amount of matter (µ) 🌡️:contentReference[oaicite:0]{index=0}. If any of these stops being uniform—for example, when a gas suddenly expands into vacuum or when a fuel-air mix explodes 🔥—the system drifts out of equilibrium, and the usual state variables temporarily lose their meaning.
📏 Intensive vs Extensive
- Extensive ➜ depend on system size: internal energy (U), volume (V), total mass (M) 🏋️♂️:contentReference[oaicite:2]{index=2}
- Intensive ➜ stay the same when you split the system: pressure (P), temperature (T), density (ρ) ❄️:contentReference[oaicite:3]{index=3}
Handy check 👉 both sides of any correct thermodynamic equation must scale the same way. Example: \( \Delta Q = \Delta U + P\,\Delta V \) — every term here is extensive 💡:contentReference[oaicite:4]{index=4}.
📜 Equation of State
A rule linking the state variables is called an equation of state. For an ideal gas the famous relation is \( P\,V = \mu\,R\,T \) 😎:contentReference[oaicite:5]{index=5}. With the amount of gas µ fixed, you really control only two variables at a time (say P and V, or T and V). Plotting P against V while holding T steady gives a smooth curve called an isotherm 📊:contentReference[oaicite:6]{index=6}.
🔥 Specific Heats of an Ideal Gas
Gases have two “heat capacities”:
- \(C_v\) (constant-volume)
- \(C_p\) (constant-pressure)
For any ideal gas they are tied together by a simple difference: \( C_p – C_v = R \) ✨:contentReference[oaicite:7]{index=7}.
Idea sketch (no worries if the symbols look heavy): start from \( \Delta Q = \Delta U + P\,\Delta V \), evaluate once at fixed V and once at fixed P, and subtract the two results—you land on the neat relation above 🙌:contentReference[oaicite:8]{index=8}.
🧭 Equilibrium vs Process Paths
A real process (like lifting a piston suddenly) can drag the gas through messy, non-equilibrium states where P and T are fuzzy. To keep math friendly, we imagine a quasi-static path instead: the gas moves so slowly that it stays in equilibrium at every step, making P, V, and T well-defined all the way 😊:contentReference[oaicite:9]{index=9}.
🎯 High-Yield Ideas for NEET
- The ideal-gas equation \( P\,V = \mu\,R\,T \) and how it trims the number of independent variables.
- Spotting intensive vs extensive quantities—often tested in conceptual MCQs.
- Relation \( C_p – C_v = R \) for an ideal gas, a frequent direct question.
- Understanding that state variables describe only equilibrium states; free expansion and explosions are classic non-examples.
- Shape and meaning of an isotherm on a P–V graph.
