Physics · Chapter 5
Study notes aligned to the official NEB syllabus.
The first law of thermodynamics is a statement of conservation of energy: it tells us that heat, work and internal energy are inter-convertible and that their total is always conserved. However, the first law says nothing about the direction in which a process will proceed. It does not forbid the following, even though none of them is ever observed:
Every one of these obeys the first law yet never happens. The second law of thermodynamics supplies the missing rule: it fixes the natural direction of spontaneous processes and sets an upper limit on the efficiency of heat engines.
It is impossible to construct a heat engine that, operating in a cycle, takes heat from a single reservoir and converts it completely into work, with no other effect.
In other words, no heat engine can be 100% efficient. Some heat must always be rejected to a colder body.
It is impossible for heat to flow spontaneously (of its own accord) from a colder body to a hotter body without the expenditure of external work.
This is why a refrigerator needs an external work input (from the mains) to pump heat "uphill" from its cold interior to the warmer room.
The two statements look different but are logically equivalent: each can be derived from the other. A violation of the Kelvin-Planck statement can always be used to build a device that violates the Clausius statement, and vice versa.
| Feature | First law | Second law |
|---|---|---|
| Basic idea | Energy is conserved | Fixes the direction of a process |
| Governs | Book-keeping of $Q$, $W$, $U$ | Feasibility and direction of heat flow |
| Heat flow | Allows heat to flow either way | Heat flows spontaneously only hot to cold |
| Engine efficiency | Places no limit | Limits it to less than 100% |
| Quantity introduced | Internal energy $U$ | Entropy $S$ |
The key point: the first law tells us how much energy is exchanged, while the second law tells us which way the exchange can go by itself.
A heat engine is a device that converts heat energy into mechanical work by working in a cycle. It operates between a hot source at temperature $T_1$ and a cold sink at temperature $T_2$ ($T_1 > T_2$). In each cycle it:
By the first law, over one complete cycle the internal energy returns to its starting value ($\Delta U = 0$), so:
$$W = Q_1 - Q_2$$
The thermal efficiency is the fraction of the absorbed heat that is converted into work:
$$\boxed{\eta = \frac{W}{Q_1} = \frac{Q_1 - Q_2}{Q_1} = 1 - \frac{Q_2}{Q_1}}$$
Since some heat $Q_2 > 0$ must always be rejected (by the second law), $\eta$ is always less than 1, that is, less than 100%.
The first law of thermodynamics is a statement of conservation of energy: it tells us that heat, work and internal energy are inter-convertible and that their total is always conserved. However, the first law says nothing about the direction in which a process will proceed. It does not forbid the following, even though none of them is ever observed:
Every one of these obeys the first law yet never happens. The second law of thermodynamics supplies the missing rule: it fixes the natural direction of spontaneous processes and sets an upper limit on the efficiency of heat engines.
It is impossible to construct a heat engine that, operating in a cycle, takes heat from a single reservoir and converts it completely into work, with no other effect.
In other words, no heat engine can be 100% efficient. Some heat must always be rejected to a colder body.
It is impossible for heat to flow spontaneously (of its own accord) from a colder body to a hotter body without the expenditure of external work.
This is why a refrigerator needs an external work input (from the mains) to pump heat "uphill" from its cold interior to the warmer room.
The two statements look different but are logically equivalent: each can be derived from the other. A violation of the Kelvin-Planck statement can always be used to build a device that violates the Clausius statement, and vice versa.
| Feature | First law | Second law |
|---|---|---|
| Basic idea | Energy is conserved | Fixes the direction of a process |
| Governs | Book-keeping of , , | Feasibility and direction of heat flow |
| Heat flow | Allows heat to flow either way | Heat flows spontaneously only hot to cold |
| Engine efficiency | Places no limit | Limits it to less than 100% |
| Quantity introduced | Internal energy | Entropy |
The key point: the first law tells us how much energy is exchanged, while the second law tells us which way the exchange can go by itself.
A heat engine is a device that converts heat energy into mechanical work by working in a cycle. It operates between a hot source at temperature and a cold sink at temperature (). In each cycle it:
By the first law, over one complete cycle the internal energy returns to its starting value (), so:
The thermal efficiency is the fraction of the absorbed heat that is converted into work:
Since some heat must always be rejected (by the second law), is always less than 1, that is, less than 100%.