1st Law

Aka. Law of Conservation of Energy. States that energy can neither be created or destroyed; can only converted from one form to another.

Originally observed for closed systems undergoing thermodynamic cycles by James Joule. And expressed as:

When a system (closed) undergoes a thermodynamic cycle, sum of the net heat supplied to the system from its surrounding and the net work input to the system from its surroundings must equal 0

$$\sum Q_\text{supplied} + \sum W_\text{input} = 0$$

Sign convention

Any sign convention can be used in the analysis. It must be mentioned clearly in the context. The final answers must not use the sign; and explicitly mention the flow of direction.

Here is the sign convention used in the lectures: For $Q$:

• Positive - Heat input. Supplied to the system
• Negative - Heat output. Rejected by the system

For $W$:

• Positive - Work output. Done by the system
• Negative - Work input. Done on the system

This convention is used in the equation: $\Delta Q - \Delta W = 0$.

Corollary 1

There exists a property of a closed system that a change in that property is equal to the sum of the net heat transfer and the work transfer during a state change. And this property is called the internal energy.

$$\Delta U = \Delta Q - \Delta W$$

Can be mathematically proven by contradiction using 1st law.

Corollary 2

The internal energy of an isolated system remain unchanged.

Corollary 3

Perpetual motion machines of the first kind are impossible.

A perpetual motion of first kind is a machine that continuously produce work without any heat input while undergoing a thermodynamic cycle.