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Specific volume is an important concept in thermodynamics. It is defined as the volume occupied by a unit mass of a substance. Mathematically, it is represented as \(v = \frac{V}{m}\), where \(V\) is the total volume and \(m\) is the mass. In the given problem, the initial specific volume of the CO2 gas can be calculated using the volume (20 m³) and mass (15 kg) initially in the cylinder. The formula yields an initial specific volume of 1.33 m³/kg. When an additional 15 kg of CO2 is added to the cylinder, the total mass becomes 30 kg while the volume remains the same, leading to a new specific volume of 0.67 m³/kg. Understanding specific volume helps in determining how much space a particular amount of gas occupies, which is crucial when dealing with gas storage and transport.

In the context of this exercise, gas leakage occurs when CO2 escapes from a pinhole in the cylinder. Over time, as gas leaks, the mass of the CO2 in the cylinder decreases. This affects the specific volume since the volume of the cylinder remains constant. The specific volume becomes larger as more gas leaks out and the mass in the cylinder decreases. This relationship can be expressed and analyzed through the formula \(v = \frac{V}{m}\). By rearranging this, we find the remaining mass \(m = \frac{V}{v}\) and subsequently determine the leaked mass. This principle helps engineers design safer and more efficient gas storage systems by accounting for potential leaks.

Carbon dioxide (CO2) is a commonly used industrial gas with distinct properties. It is colorless, odorless, and slightly acidic. Because CO2 is a greenhouse gas, its handling and storage are significant from an environmental perspective. In the exercise, CO2 is kept in a cylinder under pressure. The properties of CO2 under different pressures and temperatures influence how it behaves when stored or leaks. For instance, the density and specific volume of CO2 change with pressure. Initially, CO2 at 10 bar has a specific volume, but as it leaks and the mass decreases, the specific volume increases until it eventually equals the cylinder's capacity if all the gas were released.

The pressure and volume relationship in gases is governed by Boyle’s law, which states that the pressure of a gas is inversely proportional to its volume when temperature and amount of gas remain constant. In practical applications like this exercise, as CO2 leaks from the cylinder, the pressure can drop if the volume remains constant, or inside a flexible container, the volume might increase if pressure is held constant. For a rigid cylinder, as gas leaks out, the specific volume increases since fewer gas molecules are within the same space, and pressure tends to normalize with the atmospheric pressure outside the cylinder. Knowing these relationships helps in predicting and controlling the behavior of gases in various engineering applications.