Let's analyze each given option to determine which one accurately represents the first law of thermodynamics.
The first law of thermodynamics is a statement of the principle of the conservation of energy. It can be formulated as:
[tex]\[ \Delta U = Q - W \][/tex]
where:
- [tex]\( \Delta U \)[/tex] is the change in internal energy of the system.
- [tex]\( Q \)[/tex] is the heat added to the system.
- [tex]\( W \)[/tex] is the work done by the system.
This equation essentially means that the increase in the internal energy of a system equals the heat added to the system minus the work done by the system.
Now let's evaluate each provided option:
A. [tex]\( \Delta W = \Delta Q + \Delta U \)[/tex]
- This equation implies that the work done is equal to the sum of the heat added and the change in internal energy. This does not align with the first law of thermodynamics.
B. [tex]\( \Delta W = \Delta U - \Delta Q \)[/tex]
- This equation suggests that the work done is equal to the change in internal energy minus the heat added. This also does not fit the standard form of the first law of thermodynamics.
C. [tex]\( \Delta Q = \Delta U + W \)[/tex]
- This equation rearranges the terms but implies that the heat added is equal to the change in internal energy plus the work done by the system. This is close but not in the standard form taught in introductory thermodynamics.
D. [tex]\( \Delta U = Q - W \)[/tex]
- This equation correctly states that the change in internal energy of the system ([tex]\( \Delta U \)[/tex]) is equal to the heat added to the system ([tex]\( Q \)[/tex]) minus the work done by the system ([tex]\( W \)[/tex]). This is the classical expression of the first law of thermodynamics.
Therefore, the correct option is:
D. [tex]\( \Delta U = Q - W \)[/tex]
