To determine which formula can be used to solve problems related to the first law of thermodynamics, let's consider the fundamental principle of the first law itself.
The first law of thermodynamics states that the energy of an isolated system is conserved. In other words, the change in internal energy ([tex]\(\Delta U\)[/tex]) of a system is equal to the net heat ([tex]\(Q\)[/tex]) added to the system minus the work ([tex]\(W\)[/tex]) done by the system. This relationship is often written as:
[tex]\[ Q = \Delta U + W \][/tex]
Here, [tex]\(Q\)[/tex] represents the heat added to the system, [tex]\(\Delta U\)[/tex] represents the change in the internal energy of the system, and [tex]\(W\)[/tex] represents the work done by the system.
Let's analyze the choices given:
1. [tex]\( Q = \Delta W + U \)[/tex]:
- This formula is incorrect because it does not correctly represent the relationship among heat transfer, work done, and internal energy.
2. [tex]\( Q = U - \Delta W \)[/tex]:
- This formula is also incorrect because it incorrectly places [tex]\(U\)[/tex] (internal energy) and [tex]\(\Delta W\)[/tex] (change in work) in the equation.
3. [tex]\( Q = \Delta U + W \)[/tex]:
- This is the correct formula because it accurately states that the net heat added to the system is equal to the change in internal energy plus the work done by the system.
4. [tex]\( Q = \Delta U - W \)[/tex]:
- This formula is incorrect because it subtracts the work done by the system instead of adding it, which is not consistent with the first law of thermodynamics.
Therefore, the correct choice for solving problems related to the first law of thermodynamics is:
[tex]\[ Q = \Delta U + W \][/tex]
This is choice number 3 in the given options.
