Question

An engineer suggested that high-temperature disassociation of water be used to produce a hydrogen fuel. A reactor-separator has been designed that can accommodate temperatures as high as \(4000 \mathrm{K}\) and pressures as much as 5 atm. Water enters this reactor-separator at \(25^{\circ} \mathrm{C}\). The separator separates the various constituents in the mixture into individual streams whose temperature and pressure match those of the reactor-separator. These streams are then cooled to \(25^{\circ} \mathrm{C}\) and stored in atmospheric pressure tanks with the exception of any remaining water, which is returned to the reactor to repeat the process again. Hydrogen gas from these tanks is later burned with a stoichiometric amount of air to provide heat for an electrical power plant. The parameter that characterizes this system is the ratio of the heat released by burning the hydrogen to the amount of heat used to generate the hydrogen gas. Select the operating pressure and temperature for the reactor-separator that maximizes this ratio. Can this ratio ever be bigger than unity?

Short answer

Explain your answer based on the analysis of the relationship between temperature, pressure, and heat.

Step-by-step solution

Understand the process of water dissociation and hydrogen production

Water enters the reactor-separator at \(25^{\circ}\mathrm{C}\). High temperature dissociation of water takes place inside the reactor-separator, producing hydrogen gas. The reactor-separator can operate at temperatures as high as \(4000\mathrm{K}\) and pressures as much as 5 atm.

Determine the heat released by burning hydrogen and the heat used to generate hydrogen

We need to calculate the heat released by burning hydrogen to produce heat in the electrical power plant and the amount of heat used to generate the hydrogen gas in the reactor-separator.

Calculate the heat released in the burning of hydrogen

The heat released during the combustion of hydrogen can be estimated using the following formula: $$Q_{released}=-\Delta H_{combustion}$$ Where \(\Delta H_{combustion}\) is the enthalpy change of combustion of hydrogen.

Determine the amounts of heat used to generate hydrogen

In the process of dissociation of water and hydrogen production, energy (heat) is input into the system. This energy amount can be found using the following formula: $$Q_{input}=\Delta H_{dissociation}$$ Where \(\Delta H_{dissociation}\) is the enthalpy change of water dissociation.

Calculate the ratio and optimize it

The characteristic parameter of the system is defined as the ratio of the heat released by burning hydrogen to the amount of heat used to generate the hydrogen gas. $$\text{Ratio} = \frac{Q_{released}}{Q_{input}}$$ To maximize this ratio, we need to find the operating temperature, and pressure for the reactor-separator which will lead to the highest value of the ratio.

Analyze the possibility of the ratio being greater than unity

To determine if the ratio can ever be greater than unity, we will explore whether the heat released by burning hydrogen is ever greater than the amount of heat used to generate the hydrogen gas in the reactor-separator. In conclusion, by analyzing the relationship between temperature, pressure, and heat, we can optimize the operating conditions of the reactor-separator to maximize the efficiency of hydrogen production. Additionally, we can determine if it's possible for the ratio to ever be greater than unity.

Key concepts

Hydrogen Fuel Generation

Hydrogen fuel generation through water dissociation is a promising avenue for clean energy production. High-temperature water dissociation is an endothermic process that splits water molecules into hydrogen and oxygen gas. In order to initiate this process, substantial energy must be supplied, typically in the form of heat. The generated hydrogen can then be stored and later burned to release energy which may be used, for example, to power electrical plants.

The process described in the exercise involves a reactor-separator that operates at very high temperatures, up to 4000K, and pressures up to 5 atm. This environment facilitates the breaking of the strong H-O bonds in water to yield hydrogen gas. The efficiency of this generation process is paramount, as it determines the feasibility and sustainability of hydrogen as a fuel source, making reactor-separator optimization critical.

Heat of Combustion

The heat of combustion refers to the amount of heat energy released when a substance, such as hydrogen gas, burns in the presence of an oxidant, usually oxygen. For hydrogen, the heat of combustion is particularly high, making it an excellent energy carrier for fuel generation. This exothermic reaction releases energy that can be harnessed in various applications, including electricity generation.

Within the context of the problem, the heat released by burning hydrogen, \( Q_{released} \), is crucial for evaluating the system's efficiency. It is calculated by considering the negative enthalpy change of combustion, \( -\Delta H_{combustion} \), which is consistent with the exothermic nature of the reaction. Thus, maximizing the heat of combustion is tantamount to improving the overall energy yield of the hydrogen fuel.

Enthalpy Change

Enthalpy change, denoted as \( \Delta H \), is a measure of the heat absorbed or released during a chemical reaction at constant pressure. This property is central to understanding both the dissociation of water into hydrogen and oxygen gases, and the subsequent combustion of hydrogen.

Two critical enthalpy changes must be considered in this context: the enthalpy change of water dissociation \( \Delta H_{dissociation} \) and the enthalpy change of hydrogen combustion \( \Delta H_{combustion} \). The former is positive as energy is absorbed to break molecular bonds, while the latter is negative, indicating energy release. Monitoring and optimizing these enthalpy changes are vital to achieving a high level of thermodynamic efficiency in the hydrogen production process.

Reactor-Separator Optimization

Reactor-separator optimization involves adjusting operating conditions such as temperature and pressure to improve the efficiency and output of hydrogen production. Engineering the reactor-separator to maximize the ratio of heat released by burning hydrogen to the heat absorbed in water dissociation is a critical goal.

For the engineer's challenge in the exercise, optimization could include finding the sweet spot for temperature and pressure at which the reactor-separator operates most efficiently. This not only involves maximizing hydrogen yield but also entails considering the energy consumption for heating and the separation of gases. Enhancing the design of the reactor-separator to minimize energy input and maximize hydrogen production can have a profound impact on the viability of hydrogen as a sustainable energy resource.

Thermodynamic Efficiency

Thermodynamic efficiency is a measure of the performance of a process in converting input energy into useful output work. In the case of hydrogen fuel generation, it assesses how effectively the input heat for water dissociation translates into useful chemical energy stored in hydrogen.

The ratio described in the problem, the heat released versus heat used, \( \frac{Q_{released}}{Q_{input}} \), is a direct indicator of the system's thermodynamic efficiency. A ratio greater than unity would mean the system produces more energy than it consumes, which is an ideal but challenging target. This target is likely unattainable due to the Second Law of Thermodynamics, which implies that some energy will always be lost as waste heat in real-life processes. Therefore, improving thermodynamic efficiency is about minimizing such losses and striving for the best achievable ratio under practical conditions.