An ideal gas expands adiabatically to three times its...

An ideal gas expands adiabatically to three times its original volume. In doing so, the gas does $720 \mathrm{~J}$ of work. $(a)$ How much heat flows from the gas? $(b)$ What is the change in internal energy of the gas? ( $c$ ) Does its temperature rise or fall?

Key Concepts

Work in Thermodynamic Processes

Work in thermodynamics refers to the energy transferred when a force acts over a distance in the context of a system’s volume change. In an expansion process, the system does work on its surroundings, resulting in energy expenditure. Understanding the sign convention and the relation between work and internal energy change is crucial for analyzing processes, especially in adiabatic conditions where the work done directly decreases the system's internal energy.

Internal Energy and Temperature Relationship

For an ideal gas, the internal energy is a function solely of temperature. This means that any change in the internal energy due to work or heat transfer directly results in a change in temperature. When the internal energy decreases during an expansion process (with work done by the gas), the temperature of the gas falls correspondingly.

Adiabatic Process

An adiabatic process is one in which no heat is exchanged between a system and its surroundings. This means that during an adiabatic change, the heat transfer Q is zero; all changes in the internal energy of the system are due solely to work done by or on the system. It is a key concept in thermodynamics that simplifies energy analysis by eliminating the heat flow term from the conservation equations.

First Law of Thermodynamics

The first law of thermodynamics is a statement of energy conservation applied to thermodynamic systems, expressed as ?U = Q - W, where ?U is the change in internal energy, Q is the heat added to the system, and W is the work done by the system. In adiabatic processes, because Q is zero, the change in internal energy is directly equal to the negative of the work done, making it easier to determine how energy is redistributed within the system.

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