Thermodynamics: First Law and Energy Balance

Thermodynamics is the engineering language of energy. It tells us how heat, work, and stored energy interact in real devices such as turbines, compressors, boilers, engines, refrigerators, and everyday hardware like pressure cookers. At the center of it all is the First Law of Thermodynamics, a rigorous statement of conservation of energy applied to thermodynamic systems.

This article develops the First Law in a practical way: how to define a system, how to account for heat and work, how internal energy and enthalpy enter calculations, and how property tables and equations support energy balances.

Why the First Law matters

In mechanics, conservation of energy often appears as exchanges between kinetic and potential energy. Thermodynamics adds the idea that energy can also be stored internally in matter and transferred as heat or work. The First Law does not tell you the direction of processes or whether something is “efficient”; it only enforces accounting. If your energy balance is wrong, the model is wrong.

A useful engineering mindset is: write the energy balance first, then look up the properties you need to close it.

Systems, surroundings, and boundaries

A system is the part of the universe you choose to analyze; everything else is the surroundings. The surface separating them is the boundary. Thermodynamics is powerful because you can choose the system boundary to make the analysis easier, as long as you track the correct energy transfers.

Closed systems (control mass)

A closed system contains a fixed amount of matter. Mass does not cross the boundary, but energy can cross as heat and work. Examples include:

• A gas in a piston-cylinder device (with the piston moving)
• A sealed rigid tank being heated or cooled

Open systems (control volume)

An open system (a control volume) allows mass to cross the boundary. Energy can enter or leave with the flowing mass, as well as via heat and work. Examples include:

• Turbines, compressors, nozzles, pumps
• Heat exchangers, boilers, condensers

Choosing between closed and open system models is often the first decision in a thermodynamics problem.

Heat and work: energy in transit

The First Law distinguishes between energy stored in a system and energy crossing the boundary.

• Heat ($Q$) is energy transfer driven by a temperature difference.
• Work ($W$) is energy transfer associated with a force acting through a distance, or more broadly any organized energy transfer other than heat (shaft work, electrical work, boundary work).

A key point: heat and work are path-dependent. They are not properties of the system. You cannot say “the system has 10 kJ of heat.” You can say “10 kJ of heat was transferred.”

Sign conventions vary by discipline, but a common thermodynamics convention is:

• $Q>0$ when heat is added to the system
• $W>0$ when work is done by the system on the surroundings

Be consistent. The algebra will take care of the direction if the convention is applied carefully.

Internal energy and enthalpy: stored energy in matter

A property is something that depends only on the state, not the process. Two central thermodynamic properties are:

• Internal energy ($U$): energy stored at the microscopic level (molecular motion, interactions, etc.). We often use specific internal energy $u=U/m$.
• Enthalpy ($H$): defined as $H=U+pV$. In specific form, $h=u+pv$.

Enthalpy is especially useful in flow problems because flowing fluid must “push” its way into or out of a control volume. The $pv$ term naturally accounts for this flow work, so many open-system energy balances are cleaner in terms of $h$ than $u$.

The First Law for a closed system

For a closed system, the First Law can be written as:

$$\Delta E=Q-W$$

where the total energy $E$ often includes internal, kinetic, and potential contributions:

$$\Delta E=\Delta U+\Delta KE+\Delta PE$$

In many engineering applications, changes in kinetic and potential energy are small compared with changes in internal energy, so the balance simplifies to:

$$\Delta U=Q-W$$

Boundary work in piston-cylinder devices

A classic form of work is boundary work, the work associated with moving boundaries:

$$W_b={\int }_{V_1}^{V_2}pdV$$

If the pressure is constant during expansion or compression, this reduces to $W_b=p(V_2-V_1)$. In real processes, pressure may vary, and the integral captures that dependence.

The First Law for control volumes (open systems)

For open systems, energy can cross the boundary with mass flow. A commonly used form is the steady-flow energy equation (SFEE). In words: energy in by mass, plus heat in, equals energy out by mass, plus work out.

A practical steady-flow form is:

$$\dot{Q}-\dot{W}=\sum \dot{m}{\left(h+\frac{V^2}{2}+gz\right)}_{out}-\sum \dot{m}{\left(h+\frac{V^2}{2}+gz\right)}_{in}$$

Here:

• $\dot{m}$ is mass flow rate
• $V$ is flow speed
• $z$ is elevation
• $g$ is gravitational acceleration
• $\dot{W}$ often refers to shaft work (turbines produce it, compressors consume it)

Many devices allow useful simplifications:

• Nozzle/diffuser: $\dot{Q}\approx 0$, $\dot{W}\approx 0$, large change in kinetic energy
• Turbine: $\dot{Q}\approx 0$, change in $h$ drives shaft work, kinetic energy changes often secondary
• Compressor/pump: $\dot{Q}\approx 0$ for short residence times; work input increases $h$
• Heat exchanger: $\dot{W}\approx 0$, $\dot{Q}$ exchanged between streams; often analyze each stream separately with the other stream’s interaction represented as heat transfer

Even when simplifications are justified, they should be stated explicitly. That is part of honest energy accounting.

Property calculations: tables and equations

To use energy balances, you need properties such as $u$, $h$, $v$, and sometimes $s$ (entropy) as supporting information. These properties are not guessed; they are obtained from:

• Thermodynamic tables (steam tables for water, refrigerant tables)
• Equations of state (ideal gas law and more advanced real-gas models)

When ideal gas relations are reasonable

For many gases at moderate pressures and temperatures (air in HVAC ranges, many combustion products in some regimes), the ideal gas law is a good approximation:

$$pv=RT$$

For ideal gases, changes in internal energy and enthalpy depend mainly on temperature:

• $\Delta u\approx \int c_v(T)dT$
• $\Delta h\approx \int c_p(T)dT$

This is why ideal-gas property tables often tabulate $h(T)$ and $u(T)$ directly.

When you need steam tables (or real-fluid data)

For water and refrigerants near saturation, during phase change, or at high pressures, ideal-gas assumptions fail. In those cases, you rely on tables that provide properties at:

• Saturated states (given $T$ or $p$)
• Superheated vapor states
• Compressed (subcooled) liquid states

Energy balance problems commonly involve boiling and condensation because the latent heat effects are large, and enthalpy captures them cleanly.

Building a reliable energy balance: a practical workflow

1. Define the system clearly. Closed system or control volume? What crosses the boundary?
2. State assumptions. Steady or transient? Neglect $\Delta KE$ or $\Delta PE$? Adiabatic or not?
3. Write the First Law in the correct form. Use $U$ for closed systems, $h$ for flows.
4. Identify knowns and unknowns. Heat transfer rate, work, exit temperature, mass flow, etc.
5. Get properties from tables or equations. Use the state (two independent properties) to locate $u$ or $h$.
6. Solve and sanity-check. Signs, units, and magnitudes should match physical expectations.

Common pitfalls to avoid

• Treating heat and work as properties rather than boundary interactions
• Mixing sign conventions mid-problem
• Using $u$ where $h$ is appropriate (or vice versa) without accounting for flow work
• Neglecting kinetic energy changes in nozzles or high-speed flows
• Pulling properties without fully defining the state (for example, specifying only $T$ in a two-phase region)

Closing perspective

The First Law of Thermodynamics is not just a principle; it is a method. With a clear system definition, careful tracking of heat and work, and accurate property evaluation using tables or equations of state, you can analyze real energy systems with confidence. Energy cannot be created or destroyed, but it can move, transform, and be stored in