To solve problems related to the first law of thermodynamics, the correct formula to use is:
[tex]\[ Q = \Delta U + W \][/tex]
Here's a detailed step-by-step explanation of why this is the correct formula:
1. Understanding the First Law of Thermodynamics:
- The first law of thermodynamics is a statement of energy conservation. It tells us that the energy added to a system as heat (Q) will either increase the internal energy of the system (ΔU) or do work (W) on the surroundings.
2. Heat Added to the System (Q):
- This is the energy that is transferred to the system due to a temperature difference.
3. Change in Internal Energy (ΔU):
- This represents the change in the energy stored within the system.
4. Work Done by the System (W):
- This is the energy used by the system to do work on its surroundings.
5. Forming the Equation:
- According to the first law, the heat added to the system (Q) must equal the sum of the change in internal energy (ΔU) and the work done by the system (W). Therefore, we have:
[tex]\[ Q = \Delta U + W \][/tex]
This formula helps account for all the energy interactions in a thermodynamic process, ensuring that energy is conserved according to the first law of thermodynamics. Thus,
[tex]\[ Q = \Delta U + W \][/tex]
is the correct and complete formula to solve such problems.
