The First Law of Thermodynamics

The First Law of Thermodynamics

This boiling tea kettle represents energy in motion. The water in the kettle is turning to water vapor because heat is being transferred from the stove to the kettle. As the entire system gets hotter, work is done—from the evaporation of the water to the whistling of the kettle. (credit: Gina Hamilton)

If we are interested in how heat transfer is converted into doing work, then the conservation of energy principle is important. The first law of thermodynamics applies the conservation of energy principle to systems where heat transfer and doing work are the methods of transferring energy into and out of the system. The first law of thermodynamics states that the change in internal energy of a system equals the net heat transfer into the system minus the net work done by the system. In equation form, the first law of thermodynamics is

\(\Delta U=Q-W\text{.}\)

Here \(\Delta U\) is the change in internal energy\(U\) of the system. \(Q\) is the net heat transferred into the system—that is, \(Q\) is the sum of all heat transfer into and out of the system. \(W\) is the net work done by the system—that is, \(W\) is the sum of all work done on or by the system. We use the following sign conventions: if \(Q\) is positive, then there is a net heat transfer into the system; if \(W\) is positive, then there is net work done by the system. So positive \(Q\) adds energy to the system and positive \(W\) takes energy from the system. Thus \(\Delta U=Q-W\). Note also that if more heat transfer into the system occurs than work done, the difference is stored as internal energy. Heat engines are a good example of this—heat transfer into them takes place so that they can do work. (See the figure below.) We will now examine \(Q\), \(W\), and \(\Delta U\) further.

The first law of thermodynamics is the conservation-of-energy principle stated for a system where heat and work are the methods of transferring energy for a system in thermal equilibrium. \(Q\) represents the net heat transfer—it is the sum of all heat transfers into and out of the system. \(Q\) is positive for net heat transfer into the system. \(W\) is the total work done on and by the system. \(W\) is positive when more work is done by the system than on it. The change in the internal energy of the system, \(\Delta U\), is related to heat and work by the first law of thermodynamics, \(\Delta U=Q-W\).