91Ó°ÊÓ

A fuel cell is an electrochemical device that reacts hydrogen with oxygen from the air to produce water and DC electricity. A proposed application is replacement of the gasoline-fueled internal combustion engine in an automobile with a \(100 \mathrm{kW}\) fuel cell. You are on a summer internship with a gas supplier planning to transport hydrogen to service stations for use in cars powered by fuel cells. The hydrogen is to be transported in tube trailers, each of which has 10 tubes of length \(10.5 \mathrm{m}\) and diameter \(0.56 \mathrm{m}\). Hydrogen in the tubes at 2600 psig and an average temperature of \(298 \mathrm{K}\) is discharged at service stations to a final pressure of 55 psig. Refueling cach fuel-cell-powered automobile is estimated to require 4.0 kg of hydrogen. (a) You and your office-mate- an intern from a different university - have been asked to estimate the number of automobiles that can be refueled by one tube-trailer load of hydrogen. He does a very quick calculation and comes up with a value of 95 cars. Speculate how he did it and provide support for your speculation. What was his mistake? (b) Do the calculation using the SRK equation of state. Instead of using Eqs. \(5.3-11\) and \(5.3-13\) for the parameter \(\alpha,\) use the following correlation developed specifically for hydrogen: \(^{23}\) \(\alpha=1.202 \exp \left(-0.3228 T_{\mathrm{r}}\right)\) (c) Do the calculation using the law of corresponding states. (d) In which of the three estimates would you have the greatest confidence, and why?

Step by step solution

01

Identify the Volume of the Tube-Trailer

To calculate the volume of the tube-trailer carrying the hydrogen, utilize the formula for the volume of a cylinder, which is \( V= \pi r^2 h\). The radius (r) is half of the diameter, and the height (h) is the length of the tube. By plugging the numbers, the volume of a tube is obtained. Since the trailer contains 10 tubes, multiply the volume of a single tube by 10 to find the total volume of the tube-trailer.

02

Convert Pressure Terms

The given pressure units are in psig, which stands for pounds per square inch gauge. However, the ideal gas law requires pressure to be stated in absolute terms. To get this, one needs to convert psig to psi absolute (psia) by adding atmospheric pressure (14.7 psi), to both the beginning and final pressures.

03

Determine the Amount of Hydrogen in the Tube-Trailer

Now, use the ideal gas law, \( PV=nRT\), to calculate the number of moles (n) of hydrogen in the tube-trailer upon start and at the end. Here, P is the pressure, V is the volume, R is the ideal gas constant, and T is the temperature. After getting n in start and at the end, subtract these to find the number of moles discharged.

04

Calculate the Number of Cars that can be Refueled

It's given that refueling each fuel cell powered car requires 4.0 kg of hydrogen, this is equivalent to \( \frac{4.0 \mathrm{kg}}{2.02 \mathrm{kg/ mol}} \) moles of hydrogen. Subsequently, calculate the number of cars that can be refueled by dividing the total number of moles of hydrogen discharged by the moles of hydrogen needed per car.

05

Apply SRK Equation of State

Calculate the number of moles of hydrogen according to the SRK equation of state, and then determine the number of cars that could be refueled. Use the original volume of the tube-trailer and the given equation for the parameter \(\alpha\) in the calculation. Be cautious that the temperature is in reduced temperature \(\left(T_{\mathrm{r}}\right)\) in the equation for \(\alpha\).

06

Apply the Law of Corresponding States

Perform the similar calculation using the law of corresponding states. The critical properties of hydrogen, the critical pressure, temperature and volume, are needed for this step. After obtaining the number of moles of hydrogen, calculate the number of cars that can be refueled.

07

Evaluate the Estimations

After implementing the ideal gas law, SRK equation of state, and the law of corresponding states, compare all three estimations. Decide which estimation instills the most confidence based on the underlying assumptions of each method.

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Fuel Cell Technology

Fuel cells are fascinating devices that convert chemical energy directly into electrical energy through a chemical reaction. This process involves hydrogen and oxygen, producing water and electricity as by-products.
Unlike traditional combustion engines that burn fuel to produce energy, fuel cells rely on electrochemical reactions. This makes them more efficient and environmentally friendly.
Benefits of fuel cells include:

• Higher energy efficiency compared to internal combustion engines.
• Reduction in greenhouse gas emissions.
• Lower noise pollution.

In the context of automobiles, fuel cells present a promising alternative to gasoline engines, providing a cleaner, sustainable energy source.

SRK Equation of State

The SRK Equation of State is an essential tool in chemical engineering for predicting the behavior of gases and liquids. This model is particularly useful when dealing with real gases.
The SRK equation is formulated as:
\[ P = \frac{{RT}}{{V_m - b}} - \frac{{a \cdot \alpha}}{{V_m(V_m + b)}} \]
In this context, P is the pressure, R is the ideal gas constant, T is the temperature, V_m is the molar volume, and a, b, and \alpha are specific constants for the substance under consideration.
These expressions help predict how substances react under various pressures and temperatures. By using the adapted formula for hydrogen, the SRK model can refine hydrogen storage calculations, leading to more accurate outcomes for applications like fuel cells.

Law of Corresponding States

The Law of Corresponding States is a profound concept, stating that all gases behave similarly if they share the same reduced properties. These properties include reduced pressure, volume, and temperature.
The principle provides a universal framework, offering insights into the behaviors of different substances without detailed experimental data.
To apply this law, physicists rely on:

• Critical pressure
• Critical temperature
• Critical volume

By knowing these critical values, hydrogen's behavior can be evaluated and compared with other gases, aiding in better predictions for chemical processes like those in hydrogen transport and fuel cells.

Ideal Gas Law

The Ideal Gas Law, represented by the formula \( PV = nRT \), is a fundamental equation in chemistry to describe the behavior of an ideal gas.
Variables in the equation include pressure \( P \), volume \( V \), number of moles \( n \), ideal gas constant \( R \), and temperature \( T \).
This simple yet versatile law is often the starting point for calculations in gas-related scenarios. It assumes gases are composed of point particles that interact minimally.
While it is not perfect for real gases under high pressures or low temperatures, it provides a starting point for further, more complex calculations in chemical engineering processes, such as those involving hydrogen in fuel cells.