First & Second Laws of Thermodynamics and Their Applications Notes

First & Second Laws of Thermodynamics and Their Applications

Systems and properties, state and path functions, the zeroth and first laws, internal energy and enthalpy, specific heats, ideal-gas processes (isothermal, adiabatic, isobaric, isochoric), the second law (Kelvin–Planck and Clausius statements), heat engines, refrigerators and heat pumps, the Carnot cycle, entropy and the third law — with worked examples.

Last reviewed 4 Nov 2026 · 4 min read

1. Basic terms

Term	Meaning
System types	Open (mass and energy cross), closed (only energy crosses), isolated (neither)
Intensive / extensive properties	Independent of size (T, P, density) / depend on size (V, U, H, mass)
State function	Depends only on the state — U, H, S, G, T, P
Path function	Depends on the path — heat Q and work W
Zeroth law	If A and B are each in thermal equilibrium with C, they are in equilibrium with each other — basis of temperature measurement

2. First law — conservation of energy

FormulaFirst law (closed system)

Δ U = Q - W

Q = heat added to the system; W = work done by the system (sign convention used in engineering). For a cycle, $\oint δ Q = \oint δ W$ .

Enthalpy $H = U + P V$ ; at constant pressure, $Q_{p} = Δ H$ ; at constant volume, $Q_{v} = Δ U$ .
For an ideal gas: $C_{p} - C_{v} = R$ ; $γ = C_{p} / C_{v}$ (≈ 1.4 for air, 1.67 for monatomic gases).
A perpetual motion machine of the first kind (work without energy input) is impossible.

Ideal-gas processes

Process	Condition	Work done by gas	Heat
Isochoric	V constant	0	$Q = n C_{v} Δ T$
Isobaric	P constant	$P Δ V$	$Q = n C_{p} Δ T$
Isothermal	T constant ( $P V$ = const)	$n R T ln (V_{2} / V_{1})$	$Q = W$ (ΔU = 0)
Adiabatic (reversible)	$Q = 0$ , $P V^{γ}$ = const	$\frac{P _{1} V _{1} - P _{2} V _{2}}{γ - 1}$	0
Polytropic	$P V^{n}$ = const	$\frac{P _{1} V _{1} - P _{2} V _{2}}{n - 1}$	—

Worked Example1 — Adiabatic compression of air

Air (γ = 1.4) at 300 K and 1 bar is compressed reversibly and adiabatically to 8 bar. $T_{2} = T_{1} (P_{2} / P_{1})^{(γ - 1) / γ} = 300 \times 8^{0.2857} = 300 \times 1.811 \approx$ 543 K.

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1. Basic terms

2. First law — conservation of energy

Ideal-gas processes

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