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?
Best Answer
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.