What are the signs of q and w when a system loses heat while doing work on the surroundings?

• A. q = – , w = –
• B. q = + , w = +
• C. q = – , w = +
• D. q = + , w = –

Answer: (A)

Verified step by step guidance

1. Understand the concept of heat (q) and work (w) in thermodynamics. Heat (q) is the energy transferred due to temperature difference, while work (w) is the energy transferred when a force is applied over a distance.
2. Recall the sign conventions in thermodynamics: when a system loses heat, q is negative because energy is leaving the system. Conversely, when a system gains heat, q is positive.
3. Consider the sign of work (w): when a system does work on the surroundings, w is negative because energy is being transferred from the system to the surroundings. If work is done on the system, w is positive.
4. Apply these conventions to the given scenario: the system loses heat, so q is negative. The system does work on the surroundings, so w is negative.
5. Conclude that for a system losing heat while doing work on the surroundings, both q and w are negative, which corresponds to the option q = – , w = –.