First Law of Thermodynamics — Revision Notes

⚡ 30-Second Revision

First Law — $\Delta U = Q - W$ (where $W$ is work done by system).
Sign Conventions — $Q > 0$ (absorbed), $Q < 0$ (released); $W > 0$ (by system), $W < 0$ (on system).
Internal Energy (Ideal Gas) — $U \propto T$, so $\Delta U = 0$ for isothermal processes. $\Delta U = nC_V\Delta T$ for any process.
Work Done — Area under P-V curve. $W_{isobaric} = P\Delta V$. $W_{isothermal} = nRT \ln(V_f/V_i)$.
Isochoric — $W=0 \implies \Delta U = Q_V$.
Isobaric — $W=P\Delta V \implies Q_P = \Delta U + P\Delta V$.
Isothermal (Ideal Gas) — $\Delta U=0 \implies Q=W$.
Adiabatic — $Q=0 \implies \Delta U = -W$. Also $PV^\gamma = \text{constant}$, $TV^{\gamma-1} = \text{constant}$.
Cyclic Process — $\Delta U=0 \implies Q=W_{net}$.
Mayer's Relation — $C_P - C_V = R$.
Ratio of Specific Heats — $\gamma = C_P/C_V$. Monatomic: $\gamma = 5/3$. Diatomic: $\gamma = 7/5$.

2-Minute Revision

The First Law of Thermodynamics is the principle of energy conservation applied to thermodynamic systems, stating that the change in a system's internal energy ($\Delta U$) equals the heat ($Q$) added to it minus the work ($W$) done by it: $\Delta U = Q - W$.

Crucial sign conventions dictate $Q$ is positive for absorption and negative for release, while $W$ is positive for work done by the system and negative for work done on it. Internal energy for an ideal gas depends only on temperature, meaning $\Delta U = 0$ for isothermal processes and $\Delta U = nC_V\Delta T$ for any process.

Work done is the area under the P-V curve. Key processes include isochoric ($W=0$), isobaric ($W=P\Delta V$), isothermal ($\Delta U=0$), and adiabatic ($Q=0$). For cyclic processes, $\Delta U=0$, so $Q_{net} = W_{net}$.

Remember Mayer's relation, $C_P - C_V = R$, and the values of $\gamma = C_P/C_V$ for different types of gases (monatomic, diatomic). Mastering these concepts and sign conventions is vital for NEET problem-solving.

5-Minute Revision

The First Law of Thermodynamics is essentially the law of conservation of energy for thermodynamic systems. It quantifies the relationship between internal energy, heat, and work: $\Delta U = Q - W$. Here, $\Delta U$ is the change in the system's internal energy, $Q$ is the heat added to the system, and $W$ is the work done by the system.

Remember the critical sign conventions: $Q$ is positive if heat is absorbed, negative if released. $W$ is positive if the system does work (e.g., expansion), negative if work is done on the system (e.

g., compression).

**Internal Energy ($U$)**: For an ideal gas, $U$ depends only on temperature. Thus, for an isothermal process ($\Delta T = 0$), $\Delta U = 0$. For any process involving an ideal gas, $\Delta U = nC_V\Delta T$, where $n$ is moles, $C_V$ is molar specific heat at constant volume, and $\Delta T$ is temperature change.

**Work ($W$)**: Work done by a gas is the area under its curve on a P-V diagram.

Isobaric (constant pressure) — $W = P\Delta V$.
Isochoric (constant volume) — $W = 0$ (since $\Delta V = 0$).
Isothermal (constant temperature, ideal gas) — $W = nRT \ln(V_f/V_i)$. Since $\Delta U = 0$, then $Q = W$.
Adiabatic (no heat exchange) — $Q = 0$. So, $\Delta U = -W$. This means work is done at the expense of internal energy (cooling during expansion) or adds to internal energy (heating during compression). For adiabatic processes, $PV^\gamma = \text{constant}$ and $TV^{\gamma-1} = \text{constant}$, where $\gamma = C_P/C_V$.

Cyclic Process: If a system returns to its initial state, $\Delta U = 0$. Therefore, $Q_{net} = W_{net}$. The net work is the area enclosed by the loop on a P-V diagram.

Specific Heats: For ideal gases, $C_P - C_V = R$ (Mayer's relation). The ratio $\gamma = C_P/C_V$ is $5/3$ for monatomic, $7/5$ for diatomic, and $4/3$ for polyatomic gases.

Example: If a gas absorbs $100\,\text{J}$ of heat and expands, doing $30\,\text{J}$ of work, then $\Delta U = Q - W = 100\,\text{J} - 30\,\text{J} = 70\,\text{J}$. The internal energy increases by $70\,\text{J}$. This quick review covers the most testable aspects for NEET.

Prelims Revision Notes

The First Law of Thermodynamics is a direct consequence of the conservation of energy principle. It states that for a thermodynamic system, the change in its internal energy ($\Delta U$) is equal to the heat ($Q$) added to the system minus the work ($W$) done by the system on its surroundings. The mathematical form is $\Delta U = Q - W$.

Key Sign Conventions:

Heat ($Q$) — Positive if absorbed by the system, negative if released by the system.
Work ($W$) — Positive if done by the system (expansion), negative if done on the system (compression).

**Internal Energy ($U$)**:

A state function; depends only on the system's state (P, V, T, composition).
For an ideal gas, $U$ depends only on temperature ($T$). Thus, $\Delta U = 0$ for an isothermal process involving an ideal gas.
The change in internal energy for $n$ moles of an ideal gas is $\Delta U = nC_V\Delta T$, applicable to any process.

**Work Done ($W$)**:

A path function; depends on the process path.
Graphically, $W = \text{Area under P-V curve}$.

Thermodynamic Processes and First Law Implications (for Ideal Gas):

1
Isochoric (Constant Volume, $\Delta V = 0$) — $W = 0$. First Law: $\Delta U = Q_V$. All heat goes to internal energy.
2
Isobaric (Constant Pressure, $\Delta P = 0$) — $W = P\Delta V$. First Law: $Q_P = \Delta U + P\Delta V$. Heat contributes to both internal energy and work.
3
Isothermal (Constant Temperature, $\Delta T = 0$) — $\Delta U = 0$. First Law: $Q = W$. Heat absorbed is entirely converted to work done.

* Work done: $W = nRT \ln(V_f/V_i) = nRT \ln(P_i/P_f)$.

1
Adiabatic (No Heat Exchange, $Q = 0$) — First Law: $\Delta U = -W$. Work is done at the expense of internal energy (expansion cools) or adds to internal energy (compression heats).

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

Cyclic Process: System returns to initial state. $\Delta U = 0$. First Law: $Q_{net} = W_{net}$. Net work is the area enclosed by the cycle on a P-V diagram.

Specific Heat Capacities:

Molar specific heat at constant volume ($C_V$): $Q_V = nC_V\Delta T$.
Molar specific heat at constant pressure ($C_P$): $Q_P = nC_P\Delta T$.
Mayer's Relation — $C_P - C_V = R$ (for ideal gases).
Ratio of Specific Heats ($\gamma$) — $\gamma = C_P/C_V$.

* Monatomic gas: $C_V = \frac{3}{2}R$, $C_P = \frac{5}{2}R$, $\gamma = 5/3$. * Diatomic gas: $C_V = \frac{5}{2}R$, $C_P = \frac{7}{2}R$, $\gamma = 7/5$. * Polyatomic gas: $C_V = 3R$, $C_P = 4R$, $\gamma = 4/3$ (at high temperatures, vibrational modes contribute).

Key Points for NEET: Master sign conventions. Understand P-V diagrams (area = work). Know the implications of each process type. Apply Mayer's relation and specific heat ratios correctly.

Vyyuha Quick Recall

Quickly Understand Work: Q is for Quantity of heat, U is for Unique internal energy, W is for Work done. Remember the equation $\Delta U = Q - W$. Think of it as: 'Energy Update equals Quick heat in, minus Work out.' For signs: 'Heat IN is INcrease (positive Q), Work OUT is OUTput (positive W).'