Why the First Law matters for your chemistry exam
Ever wondered why a hot cup of tea cools down while the room gets a tiny bit warmer? That everyday magic is the first law of thermodynamics doing its job.
💡 In Simple Words: Energy can’t be created or destroyed, only moved around. When you add heat to a system, some of that heat changes the system’s internal energy, and the rest may do work, like pushing a piston.
What is the First Law of Thermodynamics?
The first law says that the total energy of an isolated system stays the same. In chemistry we write it as ΔU = q – w. Here:
- ΔU – change in internal energy, the hidden energy stored in molecules.
- q – heat added to the system (positive if heat enters).
- w – work done by the system (positive if the system pushes against something).
Think of the system like a water tank. Adding water (heat) raises the level (energy). If the tank pushes water out through a pipe (does work), the level drops a bit. The total amount of water never magically appears or disappears.
Key terms explained
Internal energy (U) is the sum of all kinetic (movement) and potential (position) energies of the particles inside. It’s not something you can see directly, but you can measure how it changes.
Heat (q) is energy transferred because of a temperature difference, like when a hot spoon warms your hand.
Work (w) in chemistry usually means pressure‑volume work: the system expands or contracts against an external pressure, like a gas inflating a balloon.
Energy balance equation in action
Let’s rearrange the first law to a form students love: q = ΔU + w. This tells you that the heat you put in equals the energy stored plus the work done.
Worked example
Suppose 500 J of heat is supplied to 1 mol of an ideal gas that expands and does 150 J of work. What’s the change in internal energy?
Using ΔU = q – w:
- q = +500 J (heat enters, so positive)
- w = +150 J (work done by the system, so positive)
ΔU = 500 J – 150 J = 350 J. The gas’s internal energy rises by 350 J.
Sign conventions at a glance
| Process | Heat (q) | Work (w) |
|---|---|---|
| Endothermic (heat absorbed) | + | depends on direction |
| Exothermic (heat released) | - | depends on direction |
| System expands (does work) | — | + |
| System compressed (work done on it) | — | - |
Remember: a plus sign means energy enters the system, a minus means it leaves.
Why the first law is useful for exam questions
Whenever a problem gives you two of the three quantities (q, w, ΔU), you can instantly find the third. It also helps you decide whether a reaction is endothermic or exothermic and whether work is being done.
Quick checklist before you finish
- Identify the system and surroundings.
- Assign correct signs to q and w.
- Use ΔU = q – w or q = ΔU + w as needed.
- Check units (usually joules).
📝 Likely Exam Questions
- Question: A 2‑mol sample of gas absorbs 800 J of heat and does 300 J of work. Calculate ΔU.
Answer: ΔU = q – w = 800 J – 300 J = 500 J. - Question: During a reaction, the system releases 250 J of heat and 100 J of work is done on it. What is the change in internal energy?
Answer: q = –250 J (heat leaves), w = –100 J (work done on system). ΔU = q – w = –250 J – (–100 J) = –150 J. - Question: Explain in one sentence why the first law does not allow a perpetual motion machine.
Answer: Because it forbids creation of energy from nothing; any energy output must equal an energy input.