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?

Key Concepts

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.