In thermodynamics, which of the following statements about the sign of work W when energy is transferred between a system and its surroundings is or are correct?

Introduction / Context:
This question assesses your understanding of sign conventions for work in thermodynamics. When studying the first law of thermodynamics, it is important to choose a consistent sign convention for heat and work. In chemistry and many physics courses, work done on the system is taken as positive and work done by the system is taken as negative. This question presents two statements involving energy transfer as work between a system and its surroundings and asks you to identify which one correctly matches this sign convention.

Given Data / Assumptions:

• W denotes work in the energy balance for a thermodynamic system.
• The convention being tested is that used in chemistry: work done on the system is positive, work done by the system is negative.
• Statement A describes energy transferred to the system from the surroundings as work.
• Statement B describes energy transferred from the system to the surroundings as work.
• No heat transfer details are given; only the sign of work is in focus.

Concept / Approach:
The common convention in chemistry is: when the surroundings compress the system (for example by decreasing its volume), they do work on the system and W is positive. When the system expands and pushes against the surroundings, the system does work on the surroundings and W is negative. This fits with the first law written as delta U = q + W, where q is heat absorbed by the system and W is work done on the system. The key is to relate phrases like to the system and from the system to the sign of W in this convention.

Step-by-Step Solution:
Step 1: Analyse statement A. It says that energy is transferred to the system from the surroundings as work, and that the surroundings do work on the system. Step 2: In the chemistry convention, work done on the system increases its internal energy and is taken as positive. Therefore, W should be positive when the surroundings perform work on the system. Step 3: Statement A also explicitly says that the value of W is positive in this case. This matches the convention and is therefore correct. Step 4: Analyse statement B. It says that energy is transferred from the system to the surroundings as work, and that work is done on the surroundings. Step 5: When the system does work on the surroundings, energy leaves the system as mechanical work, and W is negative in the chosen convention. Step 6: Statement B explicitly says that the value of W is negative in this case. This again matches the convention and is correct. Step 7: Therefore both statements A and B correctly describe the sign of W for their respective situations.

Verification / Alternative check:
A helpful way to verify the sign convention is to consider a gas in a cylinder with a movable piston. If an external force pushes the piston inwards, compressing the gas, the surroundings are doing work on the gas. The internal energy of the gas can increase and W is positive. If instead the gas expands, pushing the piston outwards against an external pressure, the gas does work on the surroundings. This reduces the energy available to remain in the system and W is negative. Applying this model directly to statements A and B shows that both are in agreement with the physical behaviour of expanding or compressing gases and the standard sign convention used in chemistry.

Why Other Options Are Wrong:
Option A alone is incomplete because it ignores the fact that statement B is also correct. Option B alone is also incomplete for the same reason. Option C, which states that both A and B are correct, matches the analysis. Option D claims that none of the statements are correct, which contradicts the standard definitions of work done on and work done by the system. Therefore, the only fully correct choice is that both A and B are correct statements about the sign of work W.

Common Pitfalls:
A common pitfall is confusing different sign conventions used in physics and engineering texts. Some textbooks define W as work done by the system, resulting in a sign convention opposite to the chemistry convention used here. Another mistake is to ignore the phrase to the system or from the system and focus only on the direction of energy transfer without relating it to the convention chosen. To avoid confusion in examinations, always check how the first law is written in the course material and apply the same convention consistently when interpreting statements about work and heat.

Final Answer:
Both given statements correctly describe the sign of work in this convention, so the correct choice is Both (A) and (B) are correct.