To solve this question, let's carefully understand the first law of thermodynamics and analyze each option:
The first law of thermodynamics is a statement on the conservation of energy. It states that the change in internal energy ([tex]\(\Delta U\)[/tex]) of a system is equal to the heat added to the system ([tex]\(Q\)[/tex]) minus the work done by the system ([tex]\(W\)[/tex]). This can be mathematically expressed as:
[tex]\[ \Delta U = Q - W \][/tex]
Now, let's examine each option and see which one matches this expression:
- Option A: [tex]\(\Delta W = \Delta Q + \Delta U\)[/tex]
[tex]\[ \Delta W = \Delta Q + \Delta U \][/tex]
This does not correctly represent the first law of thermodynamics, as it incorrectly relates work to heat and internal energy.
- Option B: [tex]\(\Delta W = \Delta U - \Delta Q\)[/tex]
[tex]\[ \Delta W = \Delta U - \Delta Q \][/tex]
This rearranges terms incorrectly, indicating work is the energy left when internal energy decreases by heat, which is not accurate.
- Option C: [tex]\(\Delta Q = \Delta U + W\)[/tex]
[tex]\[ \Delta Q = \Delta U + W \][/tex]
This incorrectly states that heat is the sum of internal energy and work done by the system, which does not align with the first law of thermodynamics.
- Option D: [tex]\(\Delta U = Q - W\)[/tex]
[tex]\[ \Delta U = Q - W \][/tex]
This correctly states that the change in internal energy is equal to the heat added to the system minus the work done by the system, which matches the first law of thermodynamics.
Thus, the correct answer is:
[tex]\[ D. \Delta U = Q - W \][/tex]
This equation accurately captures the essence of the first law of thermodynamics, where the internal energy change is the net result of heat added and work performed. Therefore, option D is the best expression of the first law of thermodynamics.
