Thermodynamics Basics Notes

Last reviewed 16 Sept 2026 · 9 min read

Basic concepts

Term	Meaning
System	Quantity of matter or region selected for study
Surroundings	Everything outside the system; separated by the boundary
Closed system (control mass)	No mass transfer; energy (heat, work) can cross — piston–cylinder
Open system (control volume)	Mass and energy cross the boundary — turbines, pumps, nozzles
Isolated system	No mass or energy transfer
Property	Observable characteristic — pressure, temperature, volume, internal energy, enthalpy, entropy
Intensive property	Independent of mass — pressure, temperature, density
Extensive property	Depends on mass — volume, energy; per unit mass it becomes specific (intensive)
State	Condition described by properties
Process	Change of state; quasi-static — sequence of equilibrium states
Cycle	Series of processes returning to the initial state
Thermodynamic equilibrium	Mechanical, thermal and chemical equilibrium

Zeroth law

If two bodies are each in thermal equilibrium with a third body, they are in thermal equilibrium with each other — the basis of temperature measurement. $T (K) = t (° C) + 273.15$ .

Work and heat

Both are energy in transition across the boundary and are path functions (inexact differentials), not properties.
Displacement work $W = \int p d V$ (area under p–V curve).
Sign convention (common in engineering): heat added to system positive, work done by system positive.

First law of thermodynamics

Energy can neither be created nor destroyed.

FormulaFirst law

For a cycle: $\oint δ Q = \oint δ W$ For a process (closed system): $Q - W = Δ U$ Internal energy $U$ is a property (point function). Enthalpy $H = U + p V$

Perpetual motion machine of the first kind (producing work without energy input) is impossible.

Ideal gas and specific heats

$p V = m R T$ ; for air $R \approx 0.287$ kJ/kg·K.
$c_{p} - c_{v} = R$ ; $γ = c_{p} / c_{v}$ (air ≈ 1.4; $c_{p} \approx 1.005$ , $c_{v} \approx 0.718$ kJ/kg·K).
For ideal gases $Δ U = m c_{v} Δ T$ ; $Δ H = m c_{p} Δ T$ .

Non-flow processes (ideal gas)

Process	Law	Work $W = \int p d V$	Heat
Constant volume (isochoric)	$p / T$ = const	0	$Q = m c_{v} (T_{2} - T_{1})$
Constant pressure (isobaric)	$V / T$ = const	$p (V_{2} - V_{1})$	$Q = m c_{p} (T_{2} - T_{1})$
Isothermal	$p V$ = const	$p_{1} V_{1} ln \frac{V _{2}}{V _{1}} = m R T ln \frac{V _{2}}{V _{1}}$	$Q = W$ ( $Δ U = 0$ )
Reversible adiabatic (isentropic)	$p V^{γ}$ = const; $\frac{T _{2}}{T _{1}} = (\frac{V _{1}}{V _{2}})^{γ - 1} = (\frac{p _{2}}{p _{1}})^{(γ - 1) / γ}$	$\frac{p _{1} V _{1} - p _{2} V _{2}}{γ - 1}$	0
Polytropic	$p V^{n}$ = const	$\frac{p _{1} V _{1} - p _{2} V _{2}}{n - 1}$	$Q = W \frac{γ - n}{γ - 1}$

Steady flow energy equation (open systems)

FormulaSFEE (per unit mass)

h_{1} + \frac{V _{1}^{2}}{2} + g z_{1} + q = h_{2} + \frac{V _{2}^{2}}{2} + g z_{2} + w

Device	Simplification
Nozzle	$q = w = 0$ → $V_{2} = 2 (h_{1} - h_{2}) + V_{1}^{2}$
Turbine (adiabatic)	$w = h_{1} - h_{2}$
Compressor/pump	$w = - (h_{2} - h_{1})$ (work input)
Throttling valve	$h_{1} = h_{2}$ (isenthalpic)
Boiler/condenser	$q = h_{2} - h_{1}$ , $w = 0$

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Basic concepts

Zeroth law

Work and heat

First law of thermodynamics

Ideal gas and specific heats

Non-flow processes (ideal gas)

Steady flow energy equation (open systems)

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