1st Law

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

Originally observed for closed systems undergoing thermodynamic cycles. Originally observed 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

$$\sum Q + \sum W = 0$$

Sign convention

Any sign convention must be mentioned clearly in the context of the analysis. And the final answers must not use the sign.

For $Q$: $$

• Positive - Heat supplied to the system
• Negative - Heat rejected by the system to its surroundings

For $W$: $$

• Positive - Work done by the system
• Negative - Work done on the system

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 a 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.