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# First law of thermodynamics

## First law of thermodynamics

The first law of thermodynamics states that an increase in internal energy of a closed system at rest is equivalent to the sum of the heat supplied to the system and the work done on the system:

The increase in internal energy of a pot of soup on the stove is equal to the heat supplied to the soup and the work done by the cook in stirring the soup (assuming no energy loss).

$$\Delta U=Q+W$$

$\Delta U$ is the change in internal energy, $Q$ is the heat supplied to the system and $W$ is the work done on the system.

The first law of thermodynamics also implies that a decrease in internal energy of the system is equivalent to the sum of the heat lost by the system and the work done by the system.

The heat lost by the system is the negative of the heat supplied to the system (i.e. $-Q$). The work done by the system is similarly represented (i.e. $-W$).

It is important to correctly determine whether the quantities specified refer to the heat lost or supplied to the system or the work done on or by the system in questions applying the first law of thermodynamics.

## Work done by a gas

The first law of thermodynamics can be applied to a system of a gas in a container.

The work done by the system (i.e. the gas) can be determined by taking the area under the graph of pressure $p$ vs volume $V$.

Work done by a gas (represented by the shaded region). The arrow represents the direction of the change (i.e. from an initial to a final state).

The work done by the gas is positive when the gas expands and the pressure decreases (the work done on the gas is negative).

The work done by the gas is negative when the gas is compressed and the pressure increases (the work done on the gas is positive).

If the pressure is constant, the work done by the gas can be explicitly calculated by:$$W=p\Delta V=p(V_{2}-V_{1})$$$\Delta V$ is the change in volume.

Recall from mechanics that $P=F/A$ and $W=Fs$.