Chapter 11 · Introduction

Chapter 11 — Thermodynamics

Heat and work are two ways of moving energy into or out of a body. This chapter writes the energy account of a gas — the first law, $\Delta U=Q-W$ — follows a gas through its basic processes, and finds why no engine can turn all of its heat into work.

Pump up a bicycle tyre quickly and feel the barrel of the pump: it is warm, although nothing hot has touched it. Open a bottle of soda and a little cloud appears in the neck — the escaping gas has cooled itself below the dew point by pushing back the air. A pressure cooker whistles, a car engine burns fuel and drives the wheels, a refrigerator pumps heat out of a cold box into a warm kitchen. In every case energy is being moved about in two different ways: as heat, which flows because of a temperature difference, and as work, done when a force moves something — a piston, a pump handle, a turbine blade.

Thermodynamics is the bookkeeping of those two flows. You will start with the idea of thermal equilibrium and the zeroth law, which is what makes a thermometer meaningful. Then you will meet the energy stored inside a body, its internal energy, and the first law: heat in, minus work out, equals the increase of internal energy. Applied to an ideal gas, the first law explains why a gas needs more heat to warm it at constant pressure than at constant volume, and what happens to the pressure, volume and temperature in isothermal, adiabatic, isochoric and isobaric changes — all drawn on a $p$–$V$ diagram where work is an area. Finally the second law tells you what the first law cannot: which way heat flows on its own, why some processes can never be undone, and why even a perfect engine — the Carnot engine — must throw some heat away.

Thermal equilibrium→Zeroth law→$\Delta U=Q-W$→$C_p-C_v=R$→$W=$ area under $p$–$V$→$pV^\gamma=$ const→Second law→$\eta=1-\dfrac{T_2}{T_1}$

🎯 By the end of this chapter you can…

explain thermal equilibrium, state the zeroth law of thermodynamics and use it to explain why thermometers work;
distinguish heat, work and internal energy, and explain why internal energy is a property of the state while heat and work depend on the process;
state and apply the first law, $\Delta U=Q-W$, with the sign convention $W$ = work done by the system;
calculate the work done by a gas, $W=\int p\,dV$, as the area under a $p$–$V$ graph;
derive Mayer's relation $C_p-C_v=R$ for an ideal gas and use $\gamma=\dfrac{C_p}{C_v}$;
describe state variables and the equation of state, and analyse quasi-static isothermal, adiabatic ($pV^\gamma=$ const), isochoric, isobaric and cyclic processes;
state the second law in the Kelvin–Planck and Clausius forms, and tell reversible from irreversible processes;
describe the Carnot cycle and use $\eta=1-\dfrac{T_2}{T_1}$, with general heat engines, refrigerators and heat pumps as a JEE Advanced extension;
tackle Board, JEE Main, JEE Advanced and NEET-style problems on thermodynamics.

An insulated beaker holds $0.50\ \text{kg}$ of water ($c=4186\ \text{J kg}^{-1}\text{K}^{-1}$). A $20\ \text{kg}$ weight falling $2.0\ \text{m}$ turns a paddle wheel that churns the water; a burner underneath can also supply heat. Choose how many times the weight is dropped and how much heat the burner gives. Before you look: if the same total energy goes in, does it matter which route it takes?

drops of the weight:10heat from burner:0 J

work done on water $W_\text{on}$—

heat supplied $Q$—

gain in internal energy—

temperature rise $\Delta T$—

Sections in this chapter

11.1

Thermal Equilibrium, the Zeroth Law and the First Law

Systems and walls, thermal equilibrium and the zeroth law, heat, work and internal energy, and the first law of thermodynamics.

$\Delta U=Q-W$

Open section →11.2

Specific Heat Capacities and Thermodynamic Processes

$C_p-C_v=R$, state variables, quasi-static isothermal, adiabatic, isochoric, isobaric and cyclic processes on the $p$–$V$ diagram.

$pV^\gamma=\text{constant}$

Open section →11.3

The Second Law, Reversible Processes and the Carnot Engine

Kelvin–Planck and Clausius statements, reversible and irreversible processes, the Carnot cycle and the greatest possible efficiency.

$\eta=1-\dfrac{T_2}{T_1}$

Open section →

✅ Before you start

You will need work done by a force and the work–energy theorem (Section 5.1), and the idea of conservation of energy (Section 5.2); the area under a graph as an integral (Section 2.2); and pressure as force per unit area (Section 9.1). From Class 11 Physics, Chapter 10 — Thermal Properties of Matter you need temperature on the kelvin scale, the ideal-gas equation $pV=nRT$ with $R=8.31\ \text{J mol}^{-1}\text{K}^{-1}$, and specific and molar specific heat capacity, $Q=mc\,\Delta T=nC\,\Delta T$. The molecular picture of internal energy (why $C_v=\tfrac32R$ for a monatomic gas) comes in Chapter 12 — Kinetic Theory; here those values are simply quoted. From mathematics you need logarithms and powers ($\ln$, $V^{\gamma}$) and significant figures (Section 1.2).

← 10.3 Heat Transfer and Newton's Law of Cooling 11.1 Thermal Equilibrium, the Zeroth Law and the First Law →