# 15.1 The first law of thermodynamics

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## Learning objectives

By the end of this section, you will be able to:

• Define the first law of thermodynamics.
• Describe how conservation of energy relates to the first law of thermodynamics.
• Identify instances of the first law of thermodynamics working in everyday situations, including biological metabolism.
• Calculate changes in the internal energy of a system, after accounting for heat transfer and work done.

The information presented in this section supports the following AP® learning objectives and science practices:

• 4.C.3.1 The student is able to make predictions about the direction of energy transfer due to temperature differences based on interactions at the microscopic level. (S.P. 6.1)
• 5.B.4.1 The student is able to describe and make predictions about the internal energy of systems. (S.P. 6.4, 7.2)
• 5.B.7.1 The student is able to predict qualitative changes in the internal energy of a thermodynamic system involving transfer of energy due to heat or work done and justify those predictions in terms of conservation of energy principles. (S.P. 6.4, 7.2)

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 [link] .) We will now examine $Q$ , $W$ , and $\Delta U$ further.

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