Overview of The First Law of Thermodynamics and Sign Conventions of Work & Heat

January 8, 2021

First Law Of Thermodynamics

The first law of thermodynamics states that:

Energy can be neither created nor destroyed but one form of energy can be converted to another form.

For example, consider a ball is placed on the top of a table initially. It will have certain potential energy ( Energy possessed by virtue of its height ) as it is at a height from the ground. When it is allowed to fall from the table this potential energy will be converted into kinetic energy ( Energy possessed by virtue of its motion ). This kinetic energy will be converted to heat, sound, etc. when it touches the ground.
In the application of the first law to a given process, the sphere of influence of the process is divided into two parts namely system and surroundings, which is illustrated in the image below.

Figure 1: Diagram to show the difference between system, surroundings and boundary.

The region in which the process occurs is the System and everything which the system interacts is the surroundings. First law of thermodynamics applies to both system and surroundings. In general,

Δ Energy of system  +  Δ Energy of surrounding  = 0

For the above example if you consider ball as a system  initial energy is potential and final energy is kinetic,but the energy is gained by surroundings as heat and sound.

Systems are of two types.

  • Open = System which exchange both mass and energy with surroundings.
  • Closed = System which exchange only energy with surroundings.

For simplification here we are considering closed systems only. In general system contains some internal energy ( in the form of attractions and vibrations ) and this tend to change when the heat is added or removed, when work is done on the system or delivered by the system.For closed systems energy transfer between system and surroundings takes place in the form of work and heat. ( where as in open systems internal energy will be associated in transit also i.e., at entry and exit of the system ). For closed systems energy changes mostly occur in internal energy. So,

Δ Energy of system = Change in internal energy  = ± Q ± W

Only change in internal energies can be found as it is hard to know the energy associated with  attractions and vibrations. Q is heat and W is work.

Sign Convention For Heat And Work

Q and W always refer to system.
  • Heat given by the system, Heat produced by the system = -Q
  • Heat given to the system, Heat supplied to the system = +Q
  • Work done by the system, work produced by the system = -W
  • Work done on the system, work given to the system = +W


Δ Internal energy  =  Q – W

Heat is given to the system and work is done by the system.

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