Internal energy in first law of thermodynamics

In analyzing closed or open systems, how can we be certain to know that the internal energy changed or is zero?

I know that the internal energy is the sum of all the energy in the system, I'm just confused on recognizing when the internal energy changes or cases when it does no change.

Because in the equation for closed systems $Q-W = \Delta U$, it is implied that whatever input or output of work or heat internal energy changes but there are some cases when the change in internal energy is zero. How is that possible? So should it mean that the work is equal to heat transferred in that situation? Does it also apply to open systems?

• One measure of internal energy changing is when the temperature changes. – Steeven Sep 18 '17 at 17:00
• So for an isothermal process it can happen that there would be no change in internal energy? – Czar Luc Sep 18 '17 at 18:50
• Yes. In an isothermal process, $\Delta U=0$. This only counts for ideal gases though! If you have non-ideal substances, where there are e.g. phase changes or chemical/structural internal changes, then internal energy may be used/absorbed for other things than to raise temperature. But for ideal gases, temperature follows internal energy closely - a change in one means a change in the other every time. – Steeven Sep 18 '17 at 18:56
• Considering that a constant temperature means that no change in internal energy, would it also apply to adiabatic processes wherein there is no heat transfer then temperature would also be constant? Would water be an example of the non-ideal substances that you are talking about? – Czar Luc Sep 18 '17 at 19:02
• Isothermal means constant temperature. Adiabatic doesn't. The temperature can easily (actually it always does) change in adiabatic processes. Don't equate heat transfer with temperature. Heat is only one type of energy transfer. – Steeven Sep 18 '17 at 19:13

The answer really depends on the system under observation. The case given in your question in which change in internal energy is zero even when some work was done by (or on) the system is certainly possible if the system is not thermally isolated (or simple isolated). A system must not be thermally isolated because some heat energy has to transfer between the surroundings and the system, if we want internal energy to remain constant after some change in volume of system is observed.

From the first law of thermodynamics,

$\Delta U=Q-W_{system}$ $\tag 1$

If $\Delta U=0$ then,

$W_{system}=Q$ $\tag 2$

Equation $(2)$ implies that if in a closed (not isolated) system, the system expands, some heat comes into the system from the surrounding to replenish the internal energy lost when the system did some work against external pressure.

From the same equation, it also follows that if due to some external agent the system gets compressed, some heat gets out of the system to relieve the system of the internal energy it gained when the external agent did some work on the system.

In simpler terms, internal energy of the system increases when work is done on the system or heat comes into the system, and decreases when work is done by the system or heat gets out of the system.

If the internal energy has to remain constant, these two factors must work oppositely. Either one should increase the internal energy while the other decreases it.

In open systems, there is no boundary between the system and surrounding. Matter becomes exchangeable. In this case there will be no boundary for the system to perform the work against. The surrounding becomes the system. For open system the terms, $Q$ and $W$, have no significance.

• I think I understand what you are saying for the closed system but it got me a little confused about your statement for the open system. Does it mean that for open systems, there would be no evidence of mechanical work, just work coming from machines such as generators,turbines, or compressors? And about Q, why would it have no significance? I've read some problems wherein there is an exchange in heat in an open system. – Czar Luc Sep 18 '17 at 18:58
• In open systems where, say water is boiling, the energy is invested into breaking the bonds of interaction between the water molecules. But since we are talking about ideal cases where internal energy is a function of temperature, we consider only closed systems for the case you have mentioned in your question. Open system in which boundary is absent, you cannot find the work done by the system because the volume of the gas that was inside the system, has now become infinite. – Mitchell Sep 18 '17 at 19:03
• Oh so that's why. I never thought of system boundaries that way, thanks. – Czar Luc Sep 18 '17 at 19:10
• Boundary can be anything which separates the system under observation from its surrounding, such that there is no exchange of matter between the two, but heat can still be transferred, and such systems are called closed systems. There are some systems where even transfer of heat is restricted. Such systems are called isolated systems. Happy learning, I wish you the best of luck learning thermodynamics.. – Mitchell Sep 18 '17 at 19:16
• In an open system, there certainly can be a boundary between the system and surroundings. Matter typically enters or leaves only through a small portion of the boundary. Over the remainder of the boundary, heat can enter and work can be done. – Chet Miller Sep 18 '17 at 20:35

A closed system is one in which no mass enters or leaves the system across its boundary with the surroundings, but work can be done at the boundary and heat can enter through portions of the boundary. An open system is one in which work can be done at the boundary, and both heat and mass can be exchanged with the surroundings across portions of the system boundary.

Your equation for the first law of thermodynamics for a closed system does indeed say that the internal energy can change only if the work done by the system on its surroundings is not equal to the heat entering the system through a portion of its boundary.

The open system (control volume) version of the first law of thermodynamics is an extension of the closed system version. It takes into account the internal energy entering the system via inlet and outlet flow streams, and it splits the work done by the system on its surroundings into two separate parts: (a) work done to force mass into or out of the system through part of its boundary and (b) all other work not related to forcing mass into or out of the system; the latter is usually referred to as "shaft work." In some cases, the open system version of the first law is written as a time dependent (transient) equation, involving the rate of change of internal energy, the rates at which mass enter and leave the system, and the rates at which work is done and heat enters through portions of the system boundary.