The internal energy of a fixed quantity of an ideal gas...

The internal energy of a fixed quantity of an ideal gas depends only on its temperature. A sample of an ideal gas is allowed to expand at a constant temperature (isothermal expansion). (a) Does the gas do work? (b) Does the gas exchange heat with its surroundings? (c) What happens to the temperature of the gas? (d) What is $\Delta U$ for the gas?

The internal energy of a fixed quantity of an ideal gas depends only on its temperature. A sample of an ideal gas is allowed to expand at a constant temperature (isothermal expansion).
(a) Does the gas do work?
(b) Does the gas exchange heat with its surroundings?
(c) What happens to the temperature of the gas?
(d) What is $\Delta U$ for the gas?

Key Concepts

Internal Energy of an Ideal Gas

In an ideal gas, the internal energy is a function solely of temperature, not volume or pressure. This means that any change in the internal energy occurs only when there is a change in temperature, which is a fundamental principle in kinetic theory and thermodynamics.

Isothermal Process

An isothermal process is one in which the temperature of the system remains constant throughout. For an ideal gas undergoing an isothermal expansion or compression, the internal energy does not change because it is dependent only on temperature. This type of process requires careful energy balance since work done must be compensated by heat exchange.

Work in Thermodynamic Processes

Work in the context of thermodynamic processes refers to the energy transferred when a system expands or contracts against an external pressure. During an isothermal expansion, the gas performs work on its surroundings by pushing against the external pressure, even as its internal energy remains constant.

Heat Transfer in Thermodynamic Processes

Heat transfer involves the exchange of energy between a system and its surroundings. In an isothermal process, because the internal energy of the gas remains constant while work is done, an equivalent amount of heat must be absorbed or released to maintain a constant temperature, as dictated by the conservation of energy.

First Law of Thermodynamics

The First Law of Thermodynamics states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. In an isothermal process for an ideal gas, this law explains why the energy provided as heat exactly balances the work done by the gas, resulting in no change in internal energy.

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