The first law of thermodynamics is the energy conservation rule for systems that can exchange heat and do work. It explains how heating a gas, compressing it, or letting it expand changes the energy stored in its particles. This law matters in engines, refrigerators, weather systems, and living cells because all of them transform energy from one form to another.
For a gas in a piston, the law connects visible motion of the piston to invisible changes in molecular motion.
Key Facts
- First law using the common physics convention: ΔU = Q - W
- Q is heat added to the system, so Q > 0 when energy enters as heat and Q < 0 when heat leaves.
- W is work done by the system, so W > 0 when a gas expands and pushes a piston outward.
- For constant pressure gas expansion or compression: W = PΔV
- For an ideal monatomic gas: U = (3/2)nRT and ΔU = (3/2)nRΔT
- If ΔU = 0, then Q = W, meaning all heat added is converted into work done by the system.
Vocabulary
- System
- The part of the universe being studied, such as the gas inside a piston-cylinder.
- Internal energy
- The total microscopic kinetic and potential energy of the particles in a system.
- Heat
- Energy transferred between a system and its surroundings because of a temperature difference.
- Work
- Energy transferred when a force moves something, such as gas pushing a piston through a distance.
- State variable
- A property that depends only on the current state of a system, such as pressure, volume, temperature, or internal energy.
Common Mistakes to Avoid
- Treating heat as something stored inside an object. Heat is energy in transit due to temperature difference, while internal energy is what the system stores.
- Using the wrong sign for work during expansion. In the convention ΔU = Q - W, expansion means the gas does work on the surroundings, so W is positive and reduces ΔU if no heat enters.
- Assuming temperature must rise whenever heat is added. If a gas expands while heat is added, some or all of the added energy may leave as work instead of increasing internal energy.
- Forgetting that PΔV work requires pressure and volume units to match. Use pascals and cubic meters so W = PΔV gives joules.
Practice Questions
- 1 A gas absorbs 600 J of heat and does 250 J of work on a piston. Using ΔU = Q - W, find the change in internal energy.
- 2 A gas expands at a constant pressure of 1.2 x 10^5 Pa from 0.030 m^3 to 0.045 m^3. Find the work done by the gas.
- 3 A sealed rigid container of gas is heated, but its volume does not change. Explain what happens to W, Q, and ΔU, and why the first law predicts this result.