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.
Understanding Physics: The First Law of Thermodynamics
A thermodynamics problem starts by choosing a system boundary. The system might be the gas inside a cylinder, the water in a kettle, or the air in a balloon. Everything outside that boundary is the surroundings.
Energy can cross the boundary in different ways. Heat crosses because there is a temperature difference. Work crosses when a force causes motion at the boundary.
A moving piston is a clear example. The gas pushes on the piston over a distance, so energy leaves the gas as work. Choosing the boundary carefully prevents many mistakes, especially when a container, piston, or heater is included in the picture.
Internal energy is not simply the temperature of an object. It includes microscopic kinetic energy from particles moving, rotating, or vibrating. It can include energy from forces between particles as well.
For an ideal gas, particle interactions are treated as negligible, so its internal energy depends only on temperature. Raising the temperature then raises the average kinetic energy of the particles. Real materials can behave differently.
When ice melts, energy enters even though the temperature stays constant. That energy separates particles from their fixed arrangement. The internal energy changes because the arrangement of particles changes, not because their average speed increases.
Heat and work are both ways to transfer energy, but they are not properties stored inside a system. A gas does not contain a certain amount of heat or a certain amount of work. It contains internal energy.
The amount of heat transferred and the work done depend on the process used. A gas can reach the same final temperature and volume by being heated slowly, heated quickly, compressed, or allowed to expand first. Its final change in internal energy is the same if the initial and final states match.
Yet the heat transfer and work can be different for each route. This is why pressure and volume graphs matter. The area beneath a process line represents the work done during that volume change.
Sign conventions need steady attention. In the common convention used here, work is positive when the system pushes outward. Expansion can cool a gas if it spends enough internal energy pushing a piston.
Compression does the reverse. Work is done on the gas, which can raise its temperature even without a heater. A bicycle pump becomes warm for this reason.
In a refrigerator, electrical work drives a compressor that forces energy out of a colder space. When solving problems, write down the system first, identify every energy transfer, then decide whether each transfer enters or leaves.
Check the final result against the physical story. Heating should not produce a lower internal energy unless the system does even more work or loses energy by another route.
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.