Ethane at 10 MPa and 100^∘ C is heated at constant pressure until its volume has increased by 60

step 1 Hi friends from ideal gas equation for constant pressure, T2 is equal to T1 into B2 upon B1, tha

Ethane at 10 MPa and 100^∘ C is heated at constant pressure...

Ethane at $10 \mathrm{MPa}$ and $100^{\circ} \mathrm{C}$ is heated at constant pressure until its volume has increased by 60 percent. Determine the final temperature using $(a)$ the ideal-gas equation of state and $(b)$ the compressibility factor. Which of these two results is the more accurate? $3-131$ Steam at $400^{\circ} \mathrm{C}$ has a specific volume of $0.02 \mathrm{~m}^{3} / \mathrm{kg}$. Determine the pressure of the steam based on $(a)$ the ideal-gas equation, $(b)$ the generalized compressibility chart, and $(c)$ the steam tables. Answers: (a) $15,529 \mathrm{kPa},$ (b) $12,574 \mathrm{kPa},$ (c) $12,515 \mathrm{kPa}$

Ethane at $10 \mathrm{MPa}$ and $100^{\circ} \mathrm{C}$ is heated at constant pressure until its volume has increased by 60 percent. Determine the final temperature using $(a)$ the ideal-gas equation of state and $(b)$ the compressibility factor. Which of these two results is the more accurate?
$3-131$ Steam at $400^{\circ} \mathrm{C}$ has a specific volume of $0.02 \mathrm{~m}^{3} / \mathrm{kg}$. Determine the pressure of the steam based on $(a)$ the ideal-gas equation, $(b)$ the generalized compressibility chart, and $(c)$ the steam tables. Answers: (a) $15,529 \mathrm{kPa},$ (b) $12,574 \mathrm{kPa},$ (c) $12,515 \mathrm{kPa}$

Key Concepts

Steam Tables

Steam tables are comprehensive data compilations that list the thermodynamic properties of water and steam over a wide range of conditions, including pressure, temperature, volume, enthalpy, and entropy. They are based on empirical data and rigorous thermodynamic relationships, offering high accuracy for calculations in engineering applications involving phase changes and the properties of water/steam. Steam tables provide more reliable results than idealized models when dealing with water in its various phases.

Generalized Compressibility Charts

Generalized compressibility charts are graphical tools that allow engineers and scientists to determine the compressibility factor (Z) for a gas based on its reduced pressure and reduced temperature. By using these charts, one can estimate the real gas behavior under various conditions without needing to directly solve complex equations of state. This makes them invaluable for preliminary design calculations and for conditions where experimental data may not be readily available.

Ideal Gas Law

The ideal gas law is an equation of state that relates pressure, volume, temperature, and the number of moles of a gas using the relation PV = nRT. It assumes that the gas molecules do not interact and occupy negligible space, making it a good approximation for many gases at low pressures and high temperatures. This law is commonly used as a first estimate for changes in state variables, such as temperature or volume under constant pressure conditions.

Compressibility Factor

The compressibility factor, commonly denoted as Z, is a correction factor used to account for deviations of a real gas from ideal behavior. It modifies the ideal gas law to yield the real gas equation of state in the form PV = Z nRT. The compressibility factor is particularly important at high pressures or low temperatures where intermolecular interactions and molecular sizes become significant, thereby making the ideal gas model less accurate.

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