A gas is confined to a cylinder fitted with a piston and an electrical heater, as shown here:

Suppose that current is supplied to the heater so that 100 J of energy is added. Consider two different situations. In case (1) the piston is allowed to move as the energy is added. In case (2) the piston is fixed so that it cannot move. (b) Identify the sign (positive, negative, or zero) of q and w in each case?

검증된 단계별 안내

Identify the system and surroundings: The gas inside the cylinder is the system, and everything outside the cylinder is the surroundings.

Understand the first law of thermodynamics: ΔU = q + w, where ΔU is the change in internal energy, q is the heat added to the system, and w is the work done by the system.

Analyze case (1) where the piston is allowed to move: When energy is added, the gas expands, doing work on the surroundings. Here, q is positive (since heat is added to the system), and w is negative (since the system does work on the surroundings).

Analyze case (2) where the piston is fixed: When energy is added, the volume does not change, so no work is done. Here, q is positive (since heat is added to the system), and w is zero (since no work is done).

Summarize the signs: In case (1), q is positive and w is negative. In case (2), q is positive and w is zero.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

First Law of Thermodynamics

The First Law of Thermodynamics states that energy cannot be created or destroyed, only transformed from one form to another. In the context of the gas in the cylinder, the energy added as heat (q) can either increase the internal energy of the gas or do work (w) on the piston, depending on whether the piston is allowed to move.

Heat (q) and Work (w)

In thermodynamics, heat (q) refers to the energy transferred due to temperature differences, while work (w) is the energy transferred when a force is applied over a distance. In the scenarios presented, the movement of the piston affects how energy is distributed between heat and work, influencing their signs based on the system's constraints.

System Constraints

The constraints of a system, such as whether the piston can move or is fixed, significantly impact the thermodynamic processes occurring. In case (1), the piston moves, allowing the gas to do work on the surroundings, while in case (2), the fixed piston means no work is done, affecting the signs of q and w differently in each scenario.