3 The First Law of Thermodynamics

Learn how the first law balances heat, work, and changes in a closed system’s energy, and how to apply it to common processes.

The

A contains a fixed amount of matter. Energy can cross its boundary, but mass cannot. The first law applies conservation of energy to this system.

Energy changes and sign convention

Using the convention that heat entering the system is positive and work done by the system is positive, the finite energy balance is

\Delta E=Q-W,\qquad \Delta E=\Delta U+\Delta KE+\Delta PE.

Here, $U$ is , $KE$ is macroscopic kinetic energy, and $PE$ is gravitational potential energy. Combining the relationships gives

\Delta U+\Delta KE+\Delta PE=Q-W.

If changes in speed and elevation are negligible, the balance reduces to $\Delta U=Q-W$ . Those changes should be treated as negligible only when that assumption is justified.

Heat and work as energy transfers

Heat and work describe ways energy crosses the system boundary; they are not properties stored in the system. is a state property, while the amounts of heat and work generally depend on the process path.

With the stated convention, heat removed from the system has $Q<0$ , and work done on the system has $W<0$ . Another convention defines work as positive when done on the system, giving $\Delta E=Q+W_{\text{on}}$ . Either convention works when applied consistently.

Work across the boundary

Work can cross a closed-system boundary in several forms, including moving- from expansion or compression, shaft work, and electrical work.

For a quasi-static process with pressure acting at a moving boundary, done by the system is

W_b=\int_{V_1}^{V_2}p\,dV.

Expansion gives positive , while compression gives negative . In this expression, $p$ is the boundary pressure for a quasi-static process. The first law itself does not require a process to be quasi-static.

Applying the energy balance

To solve an energy-balance problem:

Define the system and its initial and final states.
Identify heat and every form of work crossing the boundary.
Choose a sign convention and apply it consistently.
Apply the energy balance, checking that all terms use consistent units, such as joules or kilojoules.

For example, a gas in a piston-cylinder device receives $500\ \text{kJ}$ of heat and does $180\ \text{kJ}$ of work. If its kinetic and potential energies remain essentially unchanged, then

\Delta U=Q-W=500-180=320\ \text{kJ}.

The gas’s increases by $320\ \text{kJ}$ .

Common applications and special cases

The energy balance simplifies differently under particular conditions:

Rigid tank: If the tank’s volume is fixed, is zero. If there is no other work and changes in kinetic and potential energy are negligible, $\Delta U=Q$ .
: No heat crosses the boundary, so $Q=0$ and $\Delta E=-W$ . Work done on the system can increase its energy.
: When the system returns to its initial state, its net energy change is zero. The first law gives $Q=W$ for the net heat and work over the cycle.
Insulated stirring or electrical heating: With negligible heat transfer and negligible changes in kinetic and potential energy, work input increases the system’s . Under the convention used here, work done by the system is negative.

What the first law tells you

For a , the first law accounts for energy transferred as heat or work and changes in stored internal, kinetic, and potential energy. It determines the relationship among these transfers and changes, but by itself does not specify which direction a process will naturally occur.

The first law of thermodynamics