# What is the name of the formula ΔE = q + w?

What is the name of this formula? Google could not provide me with an answer.

$$\Delta E=q+w$$

• there might me some typing error, when i tried it provide result – Freddy Aug 9 '14 at 6:59
• @Freddy Keep in mind that Google results are influenced by your prior search history and which hits you follow the links to. Even so, this sounds textbook enough that a search should uncover something about it. – a CVn Aug 9 '14 at 22:21
• try $$\Delta Q = \Delta U + \Delta W$$ – Yomal Amarathunge Aug 11 '14 at 4:51

This is a statement of the first law of thermodynamics. The first law says that the energy of an isolated system is conserved. An isolated system is one in which neither mass nor energy is exchanged with the surroundings. This equation shows the two means by which a closed system (meaning a system in which mass is conserved but energy is not) can exchange energy with its surroundings - by heat, or by work.

$$\Delta E=q+w$$

All energy transfers can be described as either heat flow or as work done on or by a system, and therefore the total amount of heat energy that goes in or out ($q$), plus the total amount of work energy that goes in or out ($w$), must be equal to the total internal energy change of the system ($\Delta E$).

This equation is particularly important in chemical thermodynamics because we have no way of measuring the total internal energy of a real system directly - all that we can measure is the amount of heat and work that goes in or out of the system, and therefore the change in internal energy.

• To be more precise, the expression of the first law we are talking about in this thread works for closed systems, not for non-isolated (the standard name is open, by the way), because for an open system energy can also be transferred by the third way: by adding/removing matter. – Wildcat Aug 10 '14 at 5:58
• @Wildcat Good point - I was trying to avoid those details but you are right that I should be more precise. – thomij Aug 10 '14 at 9:18

The first law of thermodynamics.

It is the first law of thermodynamics, which was inducted through the repetition of many scientific observations related to the energy changes associated with chemical reactions.

Scientists observed that when the system transfers from one state to another, the total energy is neither destroyed nor created. It transfers from the system to the surrounding, this is known as the Energy Conservation Law, and one of the important results of this law is: "When the system transfer from one state to another, the change in energy of the system is constant; regardless of how the change happened." The amount of energy change depends only on the initial state of the system and final state of the system.

There are several forms of expression of the first law of thermodynamics:

"The total energy change of the system and the surrounding is zero. The energy is either destroyed nor created "

As well as:

"If we start a system in a particular situation and then make a set of changes so that the system returns to its initial state, the result of the change in energy is zero."

Usually, we do not concern about the changes that lead to the return of the system to its original state, but rather the changes in energy that associate the change in the system from the initial state to the final state.

These changes in energy are the sum of changes of all kinds; the kinetic energy of atoms, molecules or ions that make up the matter, the kinetic energy of electrons, or the different types of potential energy due to the presence of different forces of attraction or repulsion in the parts of the system. We indicate to the sum of all these kinds of energy as internal energy with the symbol $$E$$.

It is difficult to measure the internal energy of the system but what can actually be measured is the change in the internal energy of the system $$\Delta{ E}$$, which is equal to the difference between the final internal energy and the initial internal energy: $$\Delta{E} = E_2-E_1$$.

That is, the internal energy $$E$$ is a state function, so the change in $$\Delta{E}$$ depends only on its final value and its initial value.

When a physical or chemical change occurs, the energy between the system and the surrounding is exchanged in one or both of the following:

1- Change in heat energy:

a- The heat energy is flowed from the surrounding to the non-isolated system as in the endothermic reactions, where the internal energy of the system increases and the internal energy of the surroundings decreases.

b- The heat energy is flowed from the non-isolated system to the surrounding as in the exothermic reactions, where the internal energy of the system decreases and the internal energy of the surrounding increases.

2- Change in work, which is one form of energy, it is the potential energy. Here are also two cases:

a- The work may be done on the surrounding by a system as in the case of the expansion of the system, flowing energy from the system to the surrounding, that is decreases the internal energy of the system and increases the internal energy of the surrounding.

b-The surrounding conducts the work on the system as it does when the system compresses, so the energy transfers from the surrounding to the system, that is, increases the internal energy of the system and decreases the internal energy of the surrounding.

If we allow the flow of heat energy $$q$$ from the surrounding to the system, at the same time the system performs a work on the surrounding, the internal system energy increases as a result of the absorption of heat energy$$q$$, while the internal energy of the system is reduced due to the loss of the potential energy in the form of the work $$w$$, so:

The change in the internal energy of the system is thus: $$\Delta{E} = q-w$$

On the basis of this equation:

1- Heat energy $$q$$ is :

a- Positive if it flows from the surrounding to the system as in the endothermic reactions.

b- Negative if it flows from the system to the surrounding as in the endothermic reactions.

2- Work $$w$$ shall be :

a- Positive if the system conducts work on the surrounding as in the case of gas expansion.

b-Negative if the surrounding conducts the work on the system as in the case of gas compression.

If we start with gas confined in a cylinder with a piston at room temperature and put the cylinder in boiling water, for example, the heat transfers from the surrounding (boiling water) to the system (the confined gas). Due to heat transfer, the gas expands and pushes the piston that is doing the work.If the amount of heat transferred from the surrounding to the system $$\pu{400\text{Joule}}$$ , and the amount of work done by the system was $$\pu{300\text{Joule}}$$, the change in the internal energy of the system $$\Delta{E}$$, is: $$\begin{array}{ } \Delta{E}~~~=~~q~~-~w\\ ~~~~~~~~~=400-300\\ ~~~~~~~~~=\pu{+100J} \end{array}$$ In this case, the internal energy of the system increases by $$100$$ joules, while the internal energy of the surrounding is decreased by $$100$$ joules, that the change in the internal energy of the surrounding$$\Delta{E}$$ is equal to (-100 )joules.

The change in the internal energy of the surrunding can be calculated as follows:

$$q$$ for the surrounding is equal to $$(-400)$$ joules because the surrounding has lost heat energy, but $$\mathrm{w}$$ for the surrounding equals$$(-300)$$ joules because the work is done on the surrounding $$\begin{array}{ } \Delta{E}_\text{(surrounding)}~=~~~~~q~~~~~~-~~~~~w\\ ~~~~~~~~~~~~~~~~~~~~~~~~~=(-400)-(-300)\\ ~~~~~~~~~~~~~~~~~~~~~~~~~=\pu{-100J} \end{array}$$ We can see that the total internal energy of the system and the surrounding is zero ,or : $$\Delta{E}_\text{(system)} = -\Delta{E}_\text{(surrounding)}$$ $$\Delta{E}_\text{(system)} +\Delta{E}_\text{(surrounding)}=\text{zero}$$ This is one of the forms that express the first law of thermodynamics: "The total energy change of the system and the surrounding is zero. The energy is either destroyed nor created "

This is the first law of thermodynaics.

$$\Delta E=q+w$$

Delta E donates change of internal energy

q - Amount of energy supplied

w - work done by the gas

• The interpretation of quantities in this answer is just plain wrong. $\Delta E$ is a change of internal energy of a system, $q$ is heat supplied to the system, $w$ is work done on the system. – Wildcat Aug 11 '14 at 6:15
• oh yes i understood – Yomal Amarathunge Aug 11 '14 at 14:32