Why is the work done counted twice in the 1st law of thermodynamics?

[curious bishal]

On the way to prove 1st law of thermodynamics, you consider a system having initial energy E₁. Then, you supply heat q to the system. Some part of the applied heat is used for doing work.
Then, again you consider the final energy (E₂) of the system to be:
E₂=E₁+q+w
where w is the work done.

We all very well know that the work is done by the heat applied. If we add both heat applied and work done to the final energy, isn't the work done counted twice. I mean to say that the heat energy wasted in the work done is also consisted in q so why is there need to add w in the final energy E₂.

 

[jfizzix]

I think the confusion here comes from whether w is the work done on the system, or the work done by the system. These change the energy by opposite amounts.

If the system is doing work w, the energy of the system decreases by w, so

E2=E1+q-w

Then, if q=w,
E2=E1

 

[curious bishal]

I think the confusion here comes from whether w is the work done on the system, or the work done by the system. These change the energy by opposite amounts.

If the system is doing work w, the energy of the system decreases by w, so

E2=E1+q-w

Then, if q=w,
E2=E1

It doesn't give the solution to my problem. Why is the work done counted double?

 

[jfizzix]

The work is not double-counted.

If the system starts at energy E1, and you add heat q to it, the energy has changed to amount E1'= E1+q.

If the system then performs work w on its environment, it loses w units of energy, so its energy changes to E2 = E1'-w = E1+q-w.

Though some of the heat is converted into work, that doesn't affect the fact that q units of heat were added, and w units of work are extracted. Thus the net energy change is q-w.

 

[LudusRex]

The first law of thermodynamics is based on the principle of conservation of energy, which states that energy cannot be created or destroyed, it can only be converted from one form to another. In the case of a thermodynamic system, this means that the total energy of the system must remain constant.

In the scenario described, the initial energy of the system is E1. When heat q is supplied to the system, it undergoes a change in energy, resulting in a final energy of E2. However, some of the heat supplied is used to do work, which is represented by the term w in the equation E2=E1+q+w. This work done is considered as a form of energy transfer and is accounted for in the final energy of the system.

To understand why the work done is counted twice in the first law of thermodynamics, we need to consider the two forms of energy involved - heat and work. Heat is a form of energy that is transferred due to a temperature difference, while work is a form of energy that is transferred due to a force acting on a system.

In the equation E2=E1+q+w, the term q represents the heat energy supplied to the system, while the term w represents the work done. Both of these forms of energy contribute to the final energy of the system and are therefore counted twice. This is because they both play a role in the overall energy balance of the system.

Furthermore, it is important to note that the work done is not considered as a waste of energy. In fact, it is an essential part of the system's energy balance and can be converted back into heat energy if needed. Therefore, it is necessary to include the work done in the equation to accurately account for all forms of energy in the system.

In conclusion, the work done is counted twice in the first law of thermodynamics because it is a form of energy transfer that contributes to the overall energy balance of the system. It is not a waste of energy and must be included in the equation to accurately represent the conservation of energy principle.