A system consists of a sample of gas contained in a cylinder-and-piston arrangement. It undergoes the change in state shown in the drawing under two different situations: In Case 1, the cylinder and piston are perfect thermal insulators that do not allow heat to be transferred. In Case 2, the cylinder and piston are made up of a thermal conductor such as a metal, and during the state change, the cylinder gets warmer to the touch. Let 𝑞1,𝑤1, and Δ𝐸1 be the values of q, w, and Δ𝐸 for Case 1, and let 𝑞2,𝑤2, and Δ𝐸2 be the values for Case 2. b. What is the sign of 𝑤1?

검증된 단계별 안내

w represents the work done on or by the system. In thermodynamics, work done by the system on the surroundings is considered negative, while work done on the system by the surroundings is positive.

In Case 1, the system is a perfect thermal insulator, meaning no heat is exchanged with the surroundings (𝑞1 = 0).

The change in internal energy (Δ𝐸1) is related to work and heat by the first law of thermodynamics: Δ𝐸1 = 𝑞1 + 𝑤1.

Since 𝑞1 = 0, the equation simplifies to Δ𝐸1 = 𝑤1. The sign of 𝑤1 depends on whether the system does work on the surroundings or the surroundings do work on the system.

If the system expands, it does work on the surroundings, making 𝑤1 negative. If the system is compressed, the surroundings do work on it, making 𝑤1 positive. Determine the process (expansion or compression) to find the sign of 𝑤1.

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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 a closed system, the change in internal energy (ΔE) is equal to the heat added to the system (q) minus the work done by the system (w). This principle is crucial for analyzing energy changes in thermodynamic processes.

Work in Thermodynamics

In thermodynamics, work (w) is defined as the energy transferred when a force is applied over a distance. For a gas in a piston, work can be done on the gas (compression) or by the gas (expansion). The sign of work is conventionally positive when the system does work on the surroundings and negative when work is done on the system.

Adiabatic Process

An adiabatic process is one in which no heat is exchanged with the surroundings, meaning the system is thermally insulated. In Case 1, since the cylinder and piston are perfect thermal insulators, the process is adiabatic. This affects the internal energy change and the work done, as any energy change must be accounted for solely by work, influencing the sign of w1.