91Ó°ÊÓ

When working with thermodynamic problems, especially those involving gases, it's crucial to convert temperatures measured in Fahrenheit to the Kelvin scale before proceeding with calculations. The Kelvin scale is an absolute temperature scale and is used extensively in scientific calculations to ensure accuracy and consistency.

To convert Fahrenheit to Kelvin, use the formula:

• Subtract 32 from the Fahrenheit temperature.
• Multiply the result by 5/9.
• Add 273.15 to convert it to Kelvin.

For instance, converting 55°F to Kelvin is calculated as: \[ K = (55 - 32) \times \frac{5}{9} + 273.15 = 285.93 \ K \] Similarly, 85°F is converted as:\[ K = (85 - 32) \times \frac{5}{9} + 273.15 = 303.15 \ K \]
By converting temperatures to Kelvin, we can apply the equations of gas laws correctly, as it simplifies comparisons and ensures precision.

After determining the pressures at different temperatures, it's important to compare these against the maximum allowable pressure of a system to ensure safety and integrity. In thermodynamics, Gay-Lussac's Law helps predict how pressure changes with temperature for a gas at constant volume. This relationship is crucial in systems such as storage tanks, where fluctuations in temperature can affect pressure levels significantly.

The formula used is:\[ P_2 = P_1 \times \frac{T_2}{T_1} \]
Where:

• \( P_2 \) is the pressure at the new temperature.
• \( P_1 \) is the initial pressure.
• \( T_2 \), \( T_1 \) are the final and initial temperatures in Kelvin.

In our example, we found that the final pressure is \(0.0319\ psig\), which must be compared to the tank's design pressure to ensure it hasn't been exceeded.

The design pressure is often given in different units, such as inches of water—which differs from psig. Hence, conversion is necessary:1 inch of water approximates to \(0.0361\ psig\).
Thus, the maximum allowable pressure in our case is \(0.2888\ psig\), indicating that the pressure of \(0.0319\ psig\) achieved is well within safe limits.

In chemical engineering, ensuring safety is paramount, especially when dealing with volatile or flammable substances. One common safety measure is purging storage tanks with nitrogen. Purging involves removing air, which contains oxygen, from the tank and replacing it with nitrogen. This procedure is crucial for several reasons:

• Nitrogen is an inert gas, reducing the risk of combustion since it does not support burning.
• Eliminates the possibility of an explosive oxygen-fuel mixture.
• Helps maintain controlled conditions inside the tank.

Using nitrogen also maintains the integrity and longevity of the equipment by mitigating corrosion. When oxygen is present, it can react with the tank materials or the stored product, potentially leading to chemical degradation or even structural damage. Thus, the strategic use of nitrogen in purging serves as a preventive measure against accidents and maintenance issues.