If a gas expands, is the work done positive, negative, or zero?

The first law of thermodynamics then reduces to

dQ = dW + dU ⇒ dU = - dW (1)

where dW is the amount of work done by the gas and dU is the change in internal energy.

Since the gas is expanding, the work being done by the gas is positive. Eqn. (1) then implies that the change in internal energy of the system must be negative, that is, the internal energy

is decreasing. The only true statements are then:

• The work done by the gas is positive, and no heat exchange occurs.

• The internal energy of the system decreases.