Class 12 > Unit # 16:First Law of Thermodynamics > Thermodynamics & Work Done By Gas

Class 11 Physics • Thermodynamics

Thermodynamic Systems & Work Done by a Gas

Fundamental definitions of systems and surroundings, types of thermodynamic systems, and step-by-step derivation for work done during expansion.

1. Basic Thermodynamic Terminology

(i) Thermodynamics: The study of the flow of heat or any other form of energy into or out of a system as it undergoes a physical or chemical transformation.

(ii) Boundary: The physical or imaginary separation between the system and its surroundings.

(iii) Surroundings: Everything outside the boundaries of the system. This includes the rest of the universe that can interact with the system.

(iv) Thermodynamic System: A specific portion of the physical universe that is chosen for thermodynamic analysis. It is defined by boundaries and its surroundings. The system can be of any size or shape and can consist of a single substance or a combination of substances.

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2. Classification of Thermodynamic Systems

1. Open System

Both heat and matter can be exchanged with the surroundings.

Example: A cup of hot coffee (steam escapes and heat transfers to the air).

2. Closed System

Only heat can be exchanged with the surroundings, but matter cannot.

Example: A pot with a lid (heat passes through walls, but steam is trapped).

3. Isolated System

Neither heat nor matter can be exchanged with the surroundings.

Example: A well-insulated thermos flask.

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3. Derivation: Work Done by a Gas

When a gas expands, it does work on its surroundings by exerting pressure on the walls of its container. A practical application is a steam engine, where expanding steam pushes a piston to produce mechanical work.

$$W = P \Delta V$$

Where $W$ = work done ($\text{J}$), $P$ = external pressure ($\text{Pa}$), and $\Delta V$ = change in volume ($\text{m}^3$).

Step-by-Step Derivation

Consider a gas contained inside a cylinder enclosed by a moveable piston of cross-sectional area $A$.

1. Force exerted by the gas: Assuming the gas is kept at a constant pressure $P$, the outward force $F$ exerted by the gas on the piston is: $$F = P \times A$$
2. Definition of mechanical work: Work done is defined as force multiplied by displacement $S$ in the direction of the force: $$W = F \times S$$
3. Substituting Force into Work equation: $$W = (P \times A) \times S = P \times (A \times S)$$
4. Relating displacement to volume change: The product of cross-sectional area $A$ and linear displacement $S$ equals the increase in volume $\Delta V$ of the gas: $$\Delta V = A \times S$$
5. Final Expression: Substituting $\Delta V$ gives the equation for work done at constant pressure: $$W = P \Delta V$$

Note: This expression assumes that the surrounding pressure $P$ remains constant during expansion, such as when expanding against constant atmospheric pressure.

Sign Conventions for Work Done:

• Expansion ($\Delta V > 0$): Work is done by the gas on the surroundings ($W > 0$).
• Compression ($\Delta V < 0$): Work is done on the gas by the surroundings ($W < 0$).