Thermodynamics: A First-Law Energy Balance

Mechanical Engineering · CHAPTER 4 / 5

Level: introductory undergraduate · Study session: 15–20 minutes including practice.

Learning outcome: Choose a sign convention and balance heat, work and stored energy.

Before you begin: Complete earlier chapters in this discipline; revise algebra and units as needed.

1. Understand the idea

For a closed system, energy crosses the boundary as heat or work, while mass does not. Here heat entering the system is positive and work done by the system is positive. Internal energy changes when these transfers are unequal. Temperature alone does not measure total stored energy.

2. Write the model

ΔU = Q − W

Define the symbols from the worked case before substituting values. Keep units consistent, record the assumptions and round only after the calculation.

3. Follow a worked example

A gas receives 500 J of heat and does 200 J of boundary work. Its internal energy rises by 300 J. If it instead receives 300 J while doing the same work, the rise is 100 J.

4. Explore the model

Figure: calculated teaching cases; straight segments connect sampled points, not experimental observations. Read exact values below.

Illustrative scenario sweep — synthetic educational data
Heat input Q (J)	Work output W (J)	ΔU (J)
100	200	-100
300	200	100
500	200	300

Hold work at 200 J and vary heat input. The sign of ΔU changes when Q crosses W.

5. Reproduce it yourself

Copy the input cases into Excel or a notebook and name each quantity and unit.
Recalculate each result from the stated equation or rule. For qualitative cases, explain the state or partition decision instead.
Change one input, predict the direction of change, then calculate again.
Write one sentence explaining where the model stops being valid.

6. Check your understanding

If Q=0 and the gas does 100 J of work, what is ΔU?

Reveal the answer and check your work

−100 J.

Compare your result, units and reasoning. If they differ, return to the equation and test the worked case first.

7. Common mistake

This closed-system balance is not the complete steady-flow equation for a turbine.

Further study and academic note

Explore the discipline reference and further learning resources. This is an original IIMEEE introductory teaching note with synthetic examples; it is not a peer-reviewed research result or a professional design specification. Figures were constructed from the listed teaching cases. Resource links support further study and do not imply endorsement.