Three kilograms of hydrogen contained in a nondeforming...

Three kilograms of hydrogen contained in a nondeforming sealed vessel are cooled from $400^{\circ} \mathrm{C}, 400 \mathrm{kPa}(\text { abs })$ until the hydrogen pressure is $100 \mathrm{kPa}(\text { abs }) .$ Calculate the change in internal energy, enthalpy, and entropy associated with this cooling process.

Key Concepts

Constant Volume Process

A constant volume process occurs in a system where the volume is held fixed, such as in a rigid, nondeforming sealed vessel. In these processes, no work is done by expansion or compression, and any heat added or removed changes the internal energy directly. Recognizing a constant volume process is critical in thermodynamic analyses as it simplifies the relationships between heat transfer, temperature change, and state variables.

Specific Heat Capacities

Specific heat capacities, namely at constant volume (Cv) and constant pressure (Cp), quantify the amount of energy required to change the temperature of a substance by one degree under specified conditions. These properties are essential for linking temperature changes to changes in internal energy and enthalpy. They also provide insights into the molecular structure and degrees of freedom of the gas, which are pivotal for calculations in thermodynamics.

Ideal Gas Model

The ideal gas model simplifies the behavior of gases by assuming that the interactions between molecules are negligible and that the volume occupied by the gas molecules is much smaller than the container volume. This approximation allows for the use of the ideal gas law (PV = nRT) to relate pressure, volume, and temperature. It is a key concept in thermodynamics because it provides a baseline for analyzing the behavior of real gases under many conditions.

Internal Energy

Internal energy is the total energy contained within a system, encompassing the kinetic and potential energies of the molecules. For an ideal gas, changes in internal energy depend only on temperature changes and are calculated using the specific heat at constant volume. This concept is fundamental for analyzing energy transfers and the effects of temperature change in various thermodynamic processes.

Enthalpy

Enthalpy is a thermodynamic quantity defined as the sum of the internal energy and the product of pressure and volume (H = U + PV). It is especially useful when dealing with processes occurring at constant pressure. For ideal gases, the change in enthalpy is also a function only of the temperature change, and it plays a key role in understanding heat transfer during chemical reactions and phase transitions.

Thermodynamic State Functions

State functions such as internal energy, enthalpy, and entropy have values that depend solely on the state of the system and not on the path taken to reach that state. Understanding these functions is crucial because they allow us to relate measurable quantities (temperature, pressure, volume) to the energy content and disorder of the system, regardless of how the system arrived at that particular state.

Entropy

Entropy is a measure of the disorder or randomness within a system and provides a directionality to thermodynamic processes. The change in entropy during a process can be determined by considering the reversible heat transfer divided by temperature. This concept is essential to assess the feasibility of processes, as well as to quantify the dispersal of energy in both reversible and irreversible processes.

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