Thermodynamic Processes 🌡️🔥
A thermodynamic process tells the story of how a gas changes its pressure (P), volume (V), temperature (T), and energy. We love processes that move so slowly that the gas stays in perfect balance with its surroundings at every moment. We call that gentle journey a quasi-static process. In it, the external pressure and temperature differ from the gas by only a tiny amount at each step, so the gas marches along a trail of equilibrium states 🐢. :contentReference[oaicite:0]{index=0}
1. Quasi-static Process 🐢
- The piston creeps instead of racing, preventing big pressure or temperature gaps.
- This process is an ideal model; real experiments just try to get as close as possible. :contentReference[oaicite:1]{index=1}
2. Isothermal Process (temperature fixed) 🌡️
Keep the gas in contact with a huge heat reservoir so the temperature never budges. Mathematically:
\( PV = \text{constant} \) (Boyle’s law) :contentReference[oaicite:2]{index=2}
The work you get (or put in) during an isothermal change from \( (P_1,V_1) \) to \( (P_2,V_2) \) is
\( W = \mu R T \ln\!\left(\dfrac{V_2}{V_1}\right) \). :contentReference[oaicite:3]{index=3}
- No change in internal energy for an ideal gas, so any heat \(Q\) delivered to the gas turns straight into work: \( Q = W \).
- Expand ⇒ the gas absorbs heat and does work; compress ⇒ the surroundings do work and the gas releases heat.
3. Adiabatic Process (no heat exchange) ❄️
Wrap the gas in perfect insulation so no heat flows in or out. For an ideal gas:
\( PV^{\gamma} = \text{constant},\quad \gamma = \dfrac{C_p}{C_v} \). :contentReference[oaicite:4]{index=4}
Work done when the gas moves from \( (P_1,V_1) \) to \( (P_2,V_2) \):
\( W = \frac{P_2 V_2 – P_1 V_1}{\gamma-1} = \frac{\mu R\,(T_1 – T_2)}{\gamma-1}. \) :contentReference[oaicite:5]{index=5}
- If the gas expands, it spends its own internal energy doing work, so \(T_2 < T_1\). ❄️
- If you compress it, you push energy in, heating it up, so \(T_2 > T_1\).
4. Isochoric Process (volume fixed) 📦
- Volume stays locked: \( V = \text{constant} \).
- Work done \( W = 0 \) because the piston never moves.
- Any heat added changes only the internal energy and temperature. :contentReference[oaicite:6]{index=6}
5. Isobaric Process (pressure fixed) ⚖️
- Pressure stays steady: \( P = \text{constant} \).
- Work for a change \( V_1 \rightarrow V_2 \): \( W = P\,(V_2 – V_1) = \mu R (T_2 – T_1) \). :contentReference[oaicite:7]{index=7}
- Heat splits between doing work and raising internal energy.
6. Cyclic Process 🔁
- The gas returns to its starting point on the P-V diagram.
- Internal energy is a state property, so the overall change is zero: \( \Delta U = 0 \).
- Total heat absorbed equals total work done: \( Q = W \). :contentReference[oaicite:8]{index=8}
Quick P-V Picture 📈
- Isothermal and adiabatic curves both slope down, but the adiabatic curve drops steeper because no heat sneaks in to cushion the fall.
High-Yield Ideas for NEET 💡
- Boyle’s law in disguise: \( PV = \text{constant} \) for isothermal moves—easy marks! 😉
- Adiabatic rule: \( PV^{\gamma} = \text{constant} \) plus the rapid temperature drop during expansion—watch for it in numerical problems.
- Work formulas—memorise \( W = \mu R T \ln\!\left(\dfrac{V_2}{V_1}\right) \) (isothermal) and \( W = P\,(V_2 – V_1) \) (isobaric).
- Cyclic insight: \( \Delta U = 0 \) ⇒ the area inside the cycle on the P-V graph equals net work done.
- Quasi-static vs. free expansion—only the slow, balanced journey lets you use the neat equations confidently.
🎉 Happy studying! You’ve got this. 🎉
