Forms of Energy & the First Law

Separate stored energy from energy in transit, then write the closed-system First Law with a clear sign convention.

Material & Energy BalancesChemical Engineering Year 1Free preview

⏱️ About 14 min

Two tanks have the same temperature, but one is 20 m higher and the other is flowing fast. Do they contain the same total energy?

💡

The big idea: A system can store kinetic, potential, and internal energy; heat and work are not stored — they are modes of energy transfer governed by the First Law.

🎯 By the end, you'll be able to

Identify kinetic, potential, and internal energy as stored energy forms
Distinguish heat and work as energy in transit (not properties)
State an explicit sign convention for Q and W
Write and apply the closed-system First Law ΔU = Q − W

📎 Helpful to know first

Recycle, Bypass & Purge (capstone)

Stored Energy vs Energy in Transit

In material balances, we track mass. In energy balances, we track energy — but we must first separate two ideas:

Stored energy (properties of the system): kinetic energy, potential energy, and internal energy.
Energy in transit: heat Q and work W. These are not stored in the system; they are ways energy crosses the system boundary.

This distinction matters because you can tabulate or model stored energy, but you cannot assign a system a 'heat content' or 'work content'.

Three Common Stored Energy Forms

For a closed system (a fixed amount of matter), the total energy often appears as:

Kinetic energy (motion): E_k = ½mv²
Potential energy (elevation in gravity): E_p = mgz
Internal energy U (microscopic energy: molecular translation/rotation/vibration, intermolecular forces, etc.)

In many chemical-process calculations, changes in kinetic and potential energy are small compared to internal/enthalpy changes — but you should state when you neglect them.

\[ \Delta U = Q - W \]

Closed-system First Law (engineering sign convention): heat in is positive; work done by the system is positive.

⚠️ Always state your sign convention

Textbooks vary. In this course we use the common engineering convention:

Q > 0 when heat is transferred into the system.
W > 0 when work is done by the system on the surroundings.

With that convention, the First Law for a closed system is ΔU = Q − W. If you switch conventions without noticing, you will flip signs and get the wrong answer.

Interpreting ΔU = Q − W

ΔU is a change in a stored property. Q and W are path-dependent transfers across the boundary:

If you add heat (Q > 0) at constant volume, U increases (ΔU > 0).
If the system does expansion work (W > 0) with no heat input, U decreases (ΔU < 0).

In the next lessons, we'll introduce enthalpy and flow systems, but the First Law idea — conservation of energy — stays the same.

📝 Worked example: A closed, rigid tank contains a gas. During an experiment, 12.0 kJ of heat is added to the tank, and the gas does 3.5 kJ of work on a paddle wheel inside the tank (work done by the system). Using the engineering sign convention (Q in positive, W by system positive), compute ΔU.

Write the closed-system First Law with the stated convention: ΔU = Q − W
Identify signs: Q = +12.0 kJ (heat added), W = +3.5 kJ (work done by the system)
Compute: ΔU = 12.0 − 3.5 = 8.5 kJ

✓ ΔU = +8.5 kJ

✏️ Practice: A closed system undergoes a process where 20.0 kJ of heat is rejected to the surroundings and the system receives 5.0 kJ of work done on it (e.g., stirring). Using ΔU = Q − W with Q in positive and W by system positive, what is ΔU (kJ)?

Solution

Heat rejected means heat leaves: Q = −20.0 kJ
Work done on the system means work by the system is negative: W = −5.0 kJ
ΔU = Q − W = (−20.0) − (−5.0) = −15.0 kJ

Check your understanding

1. Which of the following is a property of a system (stored quantity)?

Internal energy U is stored in the system and is a property. Heat and work are modes of transfer, not properties.

2. Using the engineering convention (Q in positive, W by system positive), if a closed system has Q = +10 kJ and W = +4 kJ, then ΔU equals:

ΔU = Q − W = 10 − 4 = +6 kJ.

✅ Key takeaways

Stored energy forms commonly include kinetic, potential, and internal energy
Heat and work are energy in transit across the boundary — not stored properties
State a sign convention explicitly; here: Q in positive, W by system positive
Closed-system First Law (this convention): ΔU = Q − W

➡️ Closed-system balances are built on internal energy U, but most process equipment involves flowing streams — and that is where enthalpy becomes the natural bookkeeping variable.

Want to test yourself on this? Try the Chemical Aptitude test →