First Law of Thermodynamics

SYLLABUS

Thermodynamic systems, Work done during volume change, Heat and work; Internal energy and First law of thermodynamics, Thermodynamic processes: Adiabatic, isochoric, isothermal and isobaric, Heat capacities of an ideal gas at constant pressure and volume and relation between them, Isothermal and Adiabatic processes for an ideal gas.

What is This Chapter About?

Heat engines power our world. Every car engine, every thermal power plant, every steam turbine operates by converting heat into useful mechanical work. But how does this conversion happen? What are its limits? And what fundamental principle governs the relationship between heat, work, and the internal energy of a system?

The answers lie in thermodynamics — the science of heat and energy. Chapter 4 of NEB Grade 12 Physics introduces the First Law of Thermodynamics, one of the most universal and important laws in all of science. It is essentially the law of conservation of energy applied to thermal systems, and it forms the foundation for understanding all heat engines, refrigerators, and atmospheric processes.

This chapter carries 6 teaching hours and connects deeply with Chapter 5 (Second Law of Thermodynamics) that follows immediately after.

Key Concepts You Will Learn

Thermodynamic Systems

A thermodynamic system is any collection of matter we choose to study — a gas in a cylinder, a chemical reaction, the atmosphere. Everything outside the system is the surroundings. The system can exchange energy with its surroundings in two ways: as heat (Q) and as work (W).

Work Done During Volume Change

When a gas expands or contracts, it does work on its surroundings or has work done on it. For a gas expanding at pressure P through a small volume change dV, the work done by the gas is [latex]dW = PdV[/latex]. On a pressure-volume (P-V) diagram, this work is represented by the area under the curve — a beautifully geometric interpretation that makes abstract thermodynamics concrete and visual.

Internal Energy and the First Law

The internal energy (U) of a system is the total microscopic energy of all its molecules — their kinetic energy of random motion plus their potential energy of interaction. Unlike heat and work, internal energy is a state function — it depends only on the current state of the system, not on how it got there.

The First Law of Thermodynamics states:

[latex]dU = dQ – dW[/latex]

Or equivalently: the increase in internal energy of a system equals the heat added to it minus the work done by it. This is conservation of energy for thermal systems. It tells us that energy cannot be created or destroyed — only transferred and transformed.

Specific Heat Capacities of a Gas

Unlike solids and liquids, a gas has two distinct specific heat capacities: [latex]C_p[/latex] (at constant pressure) and [latex]C_v[/latex] (at constant volume). At constant volume, all heat goes into increasing internal energy. At constant pressure, some heat also goes into doing work against the surroundings — so [latex]C_p > C_v[/latex] always. The difference between them is given by Mayer’s relation: [latex]C_p – C_v = R[/latex], where R is the universal gas constant.

Thermodynamic Processes

The First Law applies differently depending on how a process occurs. Four key processes are studied:

In an isothermal process, temperature is constant ([latex]dT = 0[/latex]), so internal energy does not change and all heat input is converted to work: [latex]dQ = dW[/latex].

In an isochoric process, volume is constant ([latex]dV = 0[/latex]), so no work is done and all heat goes into changing internal energy: [latex]dQ = dU[/latex].

In an isobaric process, pressure is constant and both heat and work are involved in the normal way.

In an adiabatic process, no heat is exchanged with surroundings ([latex]dQ = 0[/latex]), so any work done comes entirely from internal energy: [latex]dU = -dW[/latex]. The adiabatic equation [latex]PV^\gamma = \text{constant}[/latex] governs this process, where [latex]\gamma = \frac{C_p}{C_v}[/latex].

Work Done in Isothermal and Adiabatic Processes

Deriving expressions for the work done during isothermal and adiabatic processes is an important skill in this chapter. For an isothermal process: [latex]W = nRT\ln\frac{V_2}{V_1}[/latex]. These derivations combine calculus with thermodynamic reasoning and appear frequently in NEB examinations.

Reversible and Irreversible Processes

A reversible process is one that can be exactly retraced — it proceeds through a series of equilibrium states and leaves no permanent change in the universe. In practice, all real processes are irreversible due to friction, turbulence, and heat transfer across finite temperature differences. This distinction sets up the crucial ideas of Chapter 5 (Second Law) and entropy.

Why This Chapter Matters for NEB Exams

The First Law of Thermodynamics is examined consistently in NEB Grade 12 Physics. Derivation of Mayer’s relation [latex]C_p – C_v = R[/latex], the adiabatic equation [latex]PV^\gamma = \text{constant}[/latex], and work done in isothermal and adiabatic processes are standard long-answer questions. P-V diagram interpretation questions are also common. Numerical problems involving heat, work, and internal energy changes appear in every paper.

Important Topics to Focus On

• Concept of thermodynamic systems and surroundings
• Work done by gas: [latex]dW = PdV[/latex] and area under P-V diagram
• Concept of internal energy as a state function
• Statement and mathematical form of the First Law: [latex]dU = dQ – dW[/latex]
• Specific heat capacities [latex]C_p[/latex] and [latex]C_v[/latex] and Mayer’s relation
• Four thermodynamic processes with their P-V diagrams
• Derivation of adiabatic equation [latex]PV^\gamma = \text{constant}[/latex]
• Work done in isothermal and adiabatic processes
• Distinction between reversible and irreversible processes
• Numerical problems on all of the above

Connection to Other Chapters

The First Law builds directly on Grade 11 Chapter 11 (Quantity of Heat) and Chapter 13 (Ideal Gas). It connects forward to Chapter 5 (Second Law of Thermodynamics), where the limitations of converting heat to work are explored through Carnot’s cycle and entropy. The concept of internal energy also connects to the kinetic theory of gases and the molecular interpretation of temperature. Understanding the First Law deeply makes Chapter 5 — one of the most conceptually demanding in the course — significantly more accessible.