Undergoing adiabatic expansion, 2.0 moles of hydrogen gas (H2) do 750 J of work. (a) Does the g

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Undergoing adiabatic expansion, 2.0 moles of hydrogen gas...

Undergoing adiabatic expansion, 2.0 moles of hydrogen gas $\left(\mathrm{H}_{2}\right)$ do $750 \mathrm{~J}$ of work. (a) Does the gas temperature increase or decrease? Why? (b) Find the temperature change.

Key Concepts

Degrees of Freedom in Diatomic Gases

Diatomic gases, like hydrogen (H2), typically have five active degrees of freedom at moderate temperatures (three translational and two rotational). This factor (f=5) is used to relate the change in internal energy to the change in temperature via the formula ?U = (f/2)nR?T, allowing one to calculate the temperature change resulting from the work performed during the process.

Adiabatic Process

An adiabatic process is one in which no heat is transferred into or out of the system (Q=0). In such a process, any work done by or on the gas is entirely at the expense of its internal energy, meaning that if work is performed by the gas (expansion), the gas loses internal energy which typically results in a temperature decrease.

Internal Energy of an Ideal Gas

For an ideal gas, the internal energy is directly related to its temperature and depends on the number of degrees of freedom. The internal energy can be expressed as U = (f/2)nRT, where f is the degrees of freedom, n is the number of moles, R is the ideal gas constant, and T is the absolute temperature. In the context of the adiabatic expansion, the change in internal energy directly translates to a change in temperature.

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 (?U = Q - W). For an adiabatic process where Q = 0, this simplifies to ?U = -W, linking the work done directly to the change in internal energy and thus temperature change.

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