Which of the following is a valid representation of the first law of thermodynamics?

• A. ΔU = w - q
• B. ΔU = q + w
• C. ΔU = q - w
• D. ΔU = q

Answer: (B)

Verified step by step guidance

1. Recall that the first law of thermodynamics is a statement of energy conservation, which relates the change in internal energy (\( \Delta U \)) of a system to the heat (\( q \)) added to the system and the work (\( w \)) done on or by the system.
2. Understand the sign conventions: heat added to the system is positive (\( q > 0 \)), and work done on the system is positive (\( w > 0 \)). Conversely, heat lost or work done by the system is negative.
3. Write the general form of the first law of thermodynamics as \( \Delta U = q + w \), where \( \Delta U \) is the change in internal energy, \( q \) is heat added to the system, and \( w \) is work done on the system.
4. Compare the given options to this general form. The correct representation must have \( \Delta U \) equal to the sum of heat and work, not their difference or just one term alone.
5. Conclude that the valid representation of the first law of thermodynamics from the options is \( \Delta U = q + w \).