Thermodynamics — Revision Notes

⚡ 30-Second Revision

First Law: — $Delta U = Q - W$ (Q: heat to system, W: work by system)
Work Done: — $W = int P dV$
Isobaric: — $P=\text{const}$, $W = PDelta V$
Isochoric: — $V=\text{const}$, $W=0$, $Delta U = Q$
Isothermal (Ideal Gas): — $T=\text{const}$, $Delta U=0$, $Q=W = nRT ln(V_f/V_i)$
Adiabatic (Ideal Gas): — $Q=0$, $Delta U = -W$, $PV^gamma = \text{const}$, $TV^{gamma-1} = \text{const}$
Adiabatic Work: — $W = \frac{nR(T_i - T_f)}{gamma - 1}$
Mayer's Relation: — $C_p - C_v = R$
Adiabatic Index: — $gamma = C_p/C_v$
Carnot Efficiency: — $eta = 1 - T_C/T_H$ (T in Kelvin)
Refrigerator COP: — $COP = Q_C/W = T_C/(T_H - T_C)$ (T in Kelvin)

2-Minute Revision

Thermodynamics is the study of energy transformations, especially involving heat and work. The Zeroth Law establishes temperature. The First Law is energy conservation: $Delta U = Q - W$. Remember sign conventions: $Q$ is positive if absorbed, negative if released; $W$ is positive if done by the system, negative if done on the system.

**Internal energy ($U$) for an ideal gas depends only on temperature. The Second Law introduces entropy ($S$)**, a measure of disorder, stating that total entropy of the universe increases for spontaneous processes.

It also limits heat engine efficiency. The Third Law defines absolute zero entropy.

Key processes include: isothermal (constant $T$, $Delta U=0$ for ideal gas, $Q=W$), adiabatic (no heat exchange, $Q=0$, $Delta U=-W$, $PV^gamma=\text{const}$), isobaric (constant $P$, $W=PDelta V$), and isochoric (constant $V$, $W=0$).

Work done is the area under the $P-V$ curve. Heat engines convert heat to work with efficiency $eta = 1 - T_C/T_H$ (Carnot), while refrigerators move heat using work with $COP = T_C/(T_H - T_C)$. Always convert temperatures to Kelvin for these formulas.

Also, recall Mayer's relation $C_p - C_v = R$ and $gamma = C_p/C_v$ for ideal gases.

5-Minute Revision

Start with the First Law of Thermodynamics, $Delta U = Q - W$, which is the cornerstone. $Delta U$ is the change in internal energy, $Q$ is heat added to the system, and $W$ is work done *by* the system.

Crucially, master the sign conventions: $Q > 0$ for heat absorbed, $Q < 0$ for heat released. $W > 0$ for work done by the system (expansion), $W < 0$ for work done on the system (compression). For an ideal gas, internal energy $U$ depends only on temperature $T$, so $Delta U = 0$ if $Delta T = 0$.

Next, understand the four main thermodynamic processes:

1
Isothermal Process: — $T = \text{constant}$. For an ideal gas, $Delta U = 0$, so $Q=W$. Work done: $W = nRT ln(V_f/V_i)$.
2
Adiabatic Process: — $Q = 0$. System is insulated. $Delta U = -W$. Temperature changes. Relations: $PV^gamma = \text{constant}$, $TV^{gamma-1} = \text{constant}$. Work done: $W = \frac{nR(T_i - T_f)}{gamma - 1}$.
3
Isobaric Process: — $P = \text{constant}$. Work done: $W = P(V_f - V_i)$.
4
Isochoric Process: — $V = \text{constant}$. Work done: $W = 0$. From First Law, $Delta U = Q$.

Work done can be visualized as the area under the $P-V$ curve. For a cyclic process, $Delta U = 0$, so $Q_{net} = W_{net}$.

Heat Capacities: Molar heat capacity at constant volume $C_v$ and constant pressure $C_p$. For ideal gases, Mayer's relation is $C_p - C_v = R$. The adiabatic index $gamma = C_p/C_v$. These values depend on the degrees of freedom ($f$) of the gas ($C_v = \frac{f}{2}R$). For monatomic, $f=3, gamma=5/3$. For diatomic, $f=5, gamma=7/5$.

Heat Engines and Refrigerators: A heat engine converts heat ($Q_H$) from a hot reservoir ($T_H$) into work ($W$), rejecting heat ($Q_C$) to a cold reservoir ($T_C$). Its efficiency is $eta = W/Q_H = 1 - Q_C/Q_H$.

The maximum possible efficiency is for a Carnot engine: $eta_{Carnot} = 1 - T_C/T_H$. A refrigerator does work ($W$) to move heat ($Q_C$) from a cold to a hot reservoir. Its Coefficient of Performance (COP) is $COP = Q_C/W$.

For a Carnot refrigerator, $COP_{Carnot} = T_C/(T_H - T_C)$. Always use Kelvin for temperatures in efficiency/COP formulas.

Example: A gas expands isothermally from $1,\text{L}$ to $2,\text{L}$ at $300,\text{K}$ with $n=1,\text{mol}$. $W = nRT ln(V_f/V_i) = 1 \times 8.314 \times 300 \times ln(2/1) approx 1 \times 8.314 \times 300 \times 0.693 approx 1728,\text{J}$. Since it's isothermal for an ideal gas, $Delta U = 0$, so $Q = W = 1728,\text{J}$. The gas absorbs $1728,\text{J}$ of heat and does $1728,\text{J}$ of work. This comprehensive review covers the most testable concepts for NEET.

Prelims Revision Notes

Thermodynamics: NEET Physics Revision Notes

I. Basic Concepts & Definitions:

System: — Part of universe under study. Surroundings: Everything else. Boundary: Separates system/surroundings.
Types of Systems: — Open (matter+energy exchange), Closed (energy only), Isolated (neither).
State Variables: — Properties depending only on state ($P, V, T, U, H, S$). Path Functions: Depend on path ($Q, W$).

II. Laws of Thermodynamics:

Zeroth Law: — If $A leftrightarrow C$ and $B leftrightarrow C$ (thermal equilibrium), then $A leftrightarrow B$. Basis of temperature.
First Law: — $Delta U = Q - W$.

* $Delta U$: Change in internal energy (state function, for ideal gas depends only on $T$). * $Q$: Heat added to system ($Q>0$), heat removed ($Q<0$). * $W$: Work done *by* system ($W>0$, expansion), work done *on* system ($W<0$, compression).

Second Law: — Defines direction of spontaneous processes. Total entropy of universe increases ($Delta S_{universe} > 0$). No 100% efficient heat engine possible. Heat flows from hot to cold naturally.
Third Law: — Entropy of a perfect crystal at absolute zero (0 K) is zero.

III. Thermodynamic Processes (Ideal Gas):

Work Done (General): — $W = int P dV$. Area under $P-V$ curve.
Isobaric (Constant Pressure): — $P=\text{constant}$.

* $W = P(V_f - V_i)$. * $Delta U = Q - PDelta V$.

Isochoric (Constant Volume): — $V=\text{constant}$.

* $W = 0$. * $Delta U = Q$.

Isothermal (Constant Temperature): — $T=\text{constant}$.

* For ideal gas, $Delta U = 0$. * $Q = W = nRT ln(V_f/V_i) = nRT ln(P_i/P_f)$.

Adiabatic (No Heat Exchange): — $Q=0$.

* $Delta U = -W$. * Relations: $PV^gamma = \text{constant}$, $TV^{gamma-1} = \text{constant}$, $P^{1-gamma}T^gamma = \text{constant}$. * Work done: $W = \frac{nR(T_i - T_f)}{gamma - 1} = \frac{P_iV_i - P_fV_f}{gamma - 1}$.

Cyclic Process: — System returns to initial state. $Delta U = 0$. $Q_{net} = W_{net}$.

IV. Heat Capacities & Adiabatic Index:

Molar Heat Capacity at Constant Volume ($C_v$): — $C_v = \frac{f}{2}R$ (where $f$ is degrees of freedom).

* Monatomic ($f=3$): $C_v = \frac{3}{2}R$. * Diatomic ($f=5$): $C_v = \frac{5}{2}R$.

**Molar Heat Capacity at Constant Pressure ($C_p$):**

* Mayer's Relation: $C_p - C_v = R$. * Monatomic: $C_p = \frac{5}{2}R$. * Diatomic: $C_p = \frac{7}{2}R$.

Adiabatic Index ($gamma$): — $gamma = C_p/C_v = (f+2)/f$.

* Monatomic: $gamma = 5/3 approx 1.67$. * Diatomic: $gamma = 7/5 = 1.4$.

V. Heat Engines & Refrigerators:

Heat Engine Efficiency ($eta$): — $eta = \frac{W}{Q_H} = 1 - \frac{Q_C}{Q_H}$.
Carnot Engine (Ideal): — $eta_{Carnot} = 1 - \frac{T_C}{T_H}$ (Temperatures in Kelvin).
Refrigerator Coefficient of Performance (COP): — $COP_{ref} = \frac{Q_C}{W} = \frac{Q_C}{Q_H - Q_C}$.
Carnot Refrigerator: — $COP_{Carnot, ref} = \frac{T_C}{T_H - T_C}$ (Temperatures in Kelvin).
Heat Pump COP: — $COP_{HP} = \frac{Q_H}{W} = \frac{Q_H}{Q_H - Q_C}$. Note: $COP_{HP} = COP_{ref} + 1$.

VI. Important Points for NEET:

Always convert temperatures to Kelvin for Carnot formulas.
Be precise with sign conventions for $Q$ and $W$.
Work done is positive for expansion, negative for compression.
Heat absorbed is positive, heat released is negative.
Internal energy of ideal gas depends only on temperature.
$P-V$ diagrams: Area under curve is work. Clockwise cycle = work by system. Counter-clockwise = work on system.
Free expansion: $Q=0, W=0 implies Delta U=0$. For ideal gas, $Delta T=0$. Irreversible process.

Vyyuha Quick Recall

To remember the First Law sign convention: 'Q-W' for 'Quit Working'.

Quit: Heat Quickly comes in (positive) or out (negative).
Working: System Works out (positive, expansion) or in (negative, compression).

For processes: 'I-A-I-A' (Isothermal, Adiabatic, Isobaric, Isochoric)

Isothermal: Temp constant, $Delta U=0$, Q=W.
Adiabatic: Q heat is Absent, $Delta U = -W$.
Isobaric: Pressure constant, **W=P$Delta$V**.
Adiabatic: Volume constant, W=0, $Delta U=Q$.