Why the First Law Matters in Everyday Life
Ever wondered why a hot cup of tea cools down or how a car engine turns fuel into motion? All of that is the first law of thermodynamics at work – the rule that energy never disappears, it just changes form.
💡 In Simple Words: The first law says the total energy of a closed system stays the same. If you add heat, the system’s internal energy goes up unless the system does work, like pushing a piston. If the system does work, the internal energy drops.
First Law of Thermodynamics Simple Definition
The first law of thermodynamics, also called the law of energy conservation, tells us that energy cannot be created or destroyed, only transferred or transformed. In physics, we write it as:
ΔU = Q – W
Here, ΔU is the change in internal energy (the tiny jiggling of atoms inside the system), Q is the heat added to the system, and W is the work done by the system on its surroundings.
Key Terms Explained
- Internal Energy (U): The total microscopic energy stored in the molecules of a substance – think of it as the “hidden” energy inside a bottle of soda.
- Heat (Q): Energy transferred because of a temperature difference, like the warmth moving from a hot pan to the air.
- Work (W): Energy transferred when a force moves something, such as a gas pushing a piston.
Mathematical Form and Sign Conventions
We follow the sign rule that positive Q means heat enters the system and positive W means the system does work on the surroundings. If the surroundings do work on the system (like compressing a gas), W becomes negative.
Putting it together:
| Case | Heat (Q) | Work (W) | Result on ΔU |
|---|---|---|---|
| Heating at constant volume | + | 0 | ΔU ↑ |
| Gas expands and does work | 0 | + | ΔU ↓ |
| Compression (surroundings do work) | 0 | – | ΔU ↑ |
Worked Example: Heating Water in a Closed Vessel
Suppose 1 kg of water in a sealed, rigid container is heated so that 500 kJ of heat is supplied. The container does not allow the water to expand, so no work is done (W = 0). What is the change in internal energy?
Using ΔU = Q – W:
ΔU = 500 kJ – 0 = 500 kJ. The water’s internal energy rises by 500 kJ, which shows up as a higher temperature.
Energy Flowchart
Quick Comparison: Heat vs. Work
- Heat flows because of a temperature difference; it can be transferred through conduction, convection, or radiation.
- Work involves a force moving a distance; common examples are piston movement, electrical work, or lifting an object.
Common Mistakes to Avoid
- Mixing up sign conventions – remember, heat entering is positive, work done by the system is positive.
- Treating internal energy as a property that depends on the path; it’s a state function, meaning it only cares about the start and end points.
- Forgetting that a rigid container means W = 0 because the volume cannot change.
📝 Likely Exam Questions
- State the first law of thermodynamics and explain each term.
Answer: The first law states that the change in internal energy of a system (ΔU) equals the heat added to the system (Q) minus the work done by the system (W). ΔU = Q – W. - A gas expands adiabatically (no heat exchange) and does 300 J of work. What is the change in internal energy?
Answer: Since Q = 0, ΔU = –W = –300 J. The internal energy decreases by 300 J. - Explain why the internal energy of a substance increases when it is heated at constant volume.
Answer: At constant volume, no work is done (W = 0). All the supplied heat goes into increasing the microscopic kinetic energy of molecules, raising internal energy. - In a piston‑cylinder device, 200 J of heat is supplied and the gas does 80 J of work. Calculate the final internal energy change.
Answer: ΔU = Q – W = 200 J – 80 J = 120 J. - Why is the first law called a “law of conservation of energy”?
Answer: Because it tells us that the total energy of an isolated system remains constant; energy can only change forms (heat ↔ work ↔ internal energy) but never disappears.