Where Does the Energy Go When a Gas Pushes a Piston?
Distinguish open, closed and isolated systems, state and path functions, and extensive and intensive properties, then apply the first law of thermodynamics to calculate internal energy change, heat and work, including expansion work.
How does chemistry keep track of energy?
Burning fuel, charging a battery and digesting food all move energy from one place and form to another. Thermodynamics is the bookkeeping of that energy — and its first rule is that energy is never created or destroyed, only transferred as heat and work.
This lesson covers thermodynamic systems and state functions, the first law with heat and work, and work in gas expansion.
This lesson covers thermodynamic systems and state functions, the first law with heat and work, and work in gas expansion.
What are the types of thermodynamic systems, and what are state functions?
A system is the part of the universe under study, and it is open, closed or isolated depending on whether it can exchange matter and energy with its surroundings, while state functions are properties that depend only on the present state of the system, not on how it got there.
Types of systems:
- Open system — exchanges both energy and matter; water boiling in an uncovered pan
- Closed system — exchanges energy but not matter; water in a sealed steel container
- Isolated system — exchanges neither energy nor matter; hot tea in an ideal vacuum flask
State of a system. Described by state variables such as pressure, volume, temperature and amount of substance.
State functions and path functions:
- State functions — internal energy U, enthalpy H, entropy S, Gibbs energy G, pressure, volume and temperature; any change depends only on the initial and final states
- Path functions — heat q and work w, whose values depend on the route taken
Extensive and intensive properties:
- Extensive — depend on the amount of matter; mass, volume, internal energy and enthalpy
- Intensive — independent of the amount; temperature, pressure, density and molar heat capacity
An everyday example. Reaching the third floor of a building by lift or by stairs gives the same change in height either way, like a state function, but the effort spent, like work, depends on the route.
The substance. Dividing one extensive property by another gives an intensive property — mass and volume are extensive, but density, mass divided by volume, is intensive.
Types of systems:
- Open system — exchanges both energy and matter; water boiling in an uncovered pan
- Closed system — exchanges energy but not matter; water in a sealed steel container
- Isolated system — exchanges neither energy nor matter; hot tea in an ideal vacuum flask
State of a system. Described by state variables such as pressure, volume, temperature and amount of substance.
State functions and path functions:
- State functions — internal energy U, enthalpy H, entropy S, Gibbs energy G, pressure, volume and temperature; any change depends only on the initial and final states
- Path functions — heat q and work w, whose values depend on the route taken
Extensive and intensive properties:
- Extensive — depend on the amount of matter; mass, volume, internal energy and enthalpy
- Intensive — independent of the amount; temperature, pressure, density and molar heat capacity
An everyday example. Reaching the third floor of a building by lift or by stairs gives the same change in height either way, like a state function, but the effort spent, like work, depends on the route.
The substance. Dividing one extensive property by another gives an intensive property — mass and volume are extensive, but density, mass divided by volume, is intensive.
How do you apply the first law of thermodynamics to calculate internal energy change, heat and work?
**The first law of thermodynamics states that energy is conserved, so the change in internal energy of a system equals the heat supplied to it plus the work done on it: .
Sign convention:
- q positive — heat absorbed by the system; q negative — heat released
- w positive — work done on the system; w negative — work done by the system
Expansion against a constant external pressure:**
Worked example 1. A system absorbs 500 J of heat and does 200 J of work on its surroundings:
Worked example 2. A gas expands from 2.0 L to 5.0 L against a constant external pressure of 1.0 atm:
Worked example 3. If the same gas absorbs 500 J of heat during that expansion, J.
Special cases:
- Isolated system — and , so
- Adiabatic process — , so
- Free expansion into a vacuum — , so
- Isothermal change of an ideal gas — , so
An everyday example. The weight on a pressure cooker lifting as steam builds up is work done by the gas inside on its surroundings.
The substance. Internal energy change does not depend on the path, but heat and work do — two different routes between the same states give the same with different q and w.
Sign convention:
- q positive — heat absorbed by the system; q negative — heat released
- w positive — work done on the system; w negative — work done by the system
Expansion against a constant external pressure:**
Worked example 1. A system absorbs 500 J of heat and does 200 J of work on its surroundings:
Worked example 2. A gas expands from 2.0 L to 5.0 L against a constant external pressure of 1.0 atm:
Worked example 3. If the same gas absorbs 500 J of heat during that expansion, J.
Special cases:
- Isolated system — and , so
- Adiabatic process — , so
- Free expansion into a vacuum — , so
- Isothermal change of an ideal gas — , so
An everyday example. The weight on a pressure cooker lifting as steam builds up is work done by the gas inside on its surroundings.
The substance. Internal energy change does not depend on the path, but heat and work do — two different routes between the same states give the same with different q and w.
Formula
How do you calculate the work done in a reversible isothermal expansion?
**For the reversible isothermal expansion of an ideal gas, work is , and because the temperature stays constant, and .**
Worked example. 2.0 mol of an ideal gas at 300 K expands reversibly and isothermally from 10 L to 20 L:
So the gas does 3.46 kJ of work, absorbs 3.46 kJ of heat, and its internal energy is unchanged.
Reversible versus irreversible work:
- A reversible expansion proceeds in infinitely small steps, with the external pressure always almost equal to the gas pressure
- It gives the maximum work a gas can do between two volumes at a given temperature
- The same expansion against a constant, lower external pressure does less work
An everyday example. Engineers designing turbines for power stations try to make gas expansions as close to reversible as possible, so that more work is extracted from the same fuel.
The substance. Reversible work is an ideal limit — real processes are always irreversible, so they deliver less work than this formula predicts.
Worked example. 2.0 mol of an ideal gas at 300 K expands reversibly and isothermally from 10 L to 20 L:
So the gas does 3.46 kJ of work, absorbs 3.46 kJ of heat, and its internal energy is unchanged.
Reversible versus irreversible work:
- A reversible expansion proceeds in infinitely small steps, with the external pressure always almost equal to the gas pressure
- It gives the maximum work a gas can do between two volumes at a given temperature
- The same expansion against a constant, lower external pressure does less work
An everyday example. Engineers designing turbines for power stations try to make gas expansions as close to reversible as possible, so that more work is extracted from the same fuel.
The substance. Reversible work is an ideal limit — real processes are always irreversible, so they deliver less work than this formula predicts.
Exam tip
What earns full marks on the first law of thermodynamics?
**State the sign convention at the start of every answer, then substitute q and w with their signs into .**
- Open: matter and energy; closed: energy only; isolated: neither
- State functions: U, H, S, G, P, V, T; path functions: q and w
- ;
- 1 L atm = 101.3 J
The trap. Writing work done by the gas as positive. In this convention, work done by the system is negative.
- Open: matter and energy; closed: energy only; isolated: neither
- State functions: U, H, S, G, P, V, T; path functions: q and w
- ;
- 1 L atm = 101.3 J
The trap. Writing work done by the gas as positive. In this convention, work done by the system is negative.
Did you know
Why does a bicycle pump get hot when you pump quickly?
Pushing a bicycle pump quickly compresses the air inside faster than heat can escape, which is close to an adiabatic process.
With , the first law gives . The work you do on the air raises its internal energy, so its temperature climbs and the barrel of the pump warms up.
The reverse happens when compressed gas rushes out of a spray can: it does work on its surroundings, its internal energy falls, and the nozzle feels cold.
With , the first law gives . The work you do on the air raises its internal energy, so its temperature climbs and the barrel of the pump warms up.
The reverse happens when compressed gas rushes out of a spray can: it does work on its surroundings, its internal energy falls, and the nozzle feels cold.
Exam relevance
How do JEE Main and NEET test systems, state functions and the first law?
Thermodynamics is a recurring chapter in both JEE Main and NEET, and because it is also studied in Class 11 Physics, its ideas are tested from both sides.
What gets asked. Classifying systems and properties, identifying state and path functions, **calculations using , work against constant pressure and in reversible isothermal expansion, and special cases such as adiabatic and free expansion.
Question types. Mostly numerical and single-correct questions, with graph-based questions on pressure-volume diagrams.
Why it matters later. The first law leads directly to enthalpy, Hess's law, entropy and Gibbs energy in the rest of this chapter, and to energy calculations in Electrochemistry.
The trap that costs marks. Mixing up the chemistry and physics sign conventions for work** — check which convention a question follows before substituting.
What gets asked. Classifying systems and properties, identifying state and path functions, **calculations using , work against constant pressure and in reversible isothermal expansion, and special cases such as adiabatic and free expansion.
Question types. Mostly numerical and single-correct questions, with graph-based questions on pressure-volume diagrams.
Why it matters later. The first law leads directly to enthalpy, Hess's law, entropy and Gibbs energy in the rest of this chapter, and to energy calculations in Electrochemistry.
The trap that costs marks. Mixing up the chemistry and physics sign conventions for work** — check which convention a question follows before substituting.
Key takeaways
What must you be able to do from this lesson?
- Systems and properties: open, closed and isolated systems; state versus path functions; extensive versus intensive properties
- First law: , with against constant pressure
- Reversible isothermal work: , with and
A gas absorbs 250 J of heat while 100 J of work is done on it. What is the change in its internal energy?
- First law: , with against constant pressure
- Reversible isothermal work: , with and
A gas absorbs 250 J of heat while 100 J of work is done on it. What is the change in its internal energy?