Isentropic Compressible Flow for Non-Ideal Gas Models for a Venturi

2004 ◽  
Vol 126 (2) ◽  
pp. 238-244 ◽  
Author(s):  
Kenneth C. Cornelius ◽  
Kartik Srinivas
Keyword(s):  
Mach Number ◽  
Equation Of State ◽  
Compressible Flow ◽  
Mathematical Formulation ◽  
Compressibility Factor ◽  
Ideal Gas ◽  
Ideal Gas Law ◽  
Thermodynamic Variables ◽  
Analytical Result ◽  
The Ideal

The non-ideal gas equations and mathematical formulation developed in this work using the compressibility factor in the equation of state closely resemble the derivations used for the ideal gas mathematical formulation for a direct comparison of the differences between the ideal versus the non-ideal gas law. The local Mach number is defined for the non-ideal gas. The plenum total variables used in compressible flow are expressed in terms of the local Mach number for the polytrope and Rayleigh models. A power law relationship is derived between the thermodynamic variables that allow an analytical result for the mass flow under certain constraints.

Making sense of sensemaking: using the sensemaking epistemic game to investigate student discourse during a collaborative gas law activity

2021 ◽  
Author(s):  
Kevin H. Hunter ◽  
Jon-Marc G. Rodriguez ◽  
Nicole M. Becker
Keyword(s):  
Problem Solving ◽  
Conceptual Understanding ◽  
Ideal Gas ◽  
Interactive Simulation ◽  
Structural Components ◽  
Student Discourse ◽  
Coding Scheme ◽  
Making Sense ◽  
Ideal Gas Law ◽  
The Ideal

Beyond students’ ability to manipulate variables and solve problems, chemistry instructors are also interested in students developing a deeper conceptual understanding of chemistry, that is, engaging in the process of sensemaking. The concept of sensemaking transcends problem-solving and focuses on students recognizing a gap in knowledge and working to construct an explanation that resolves this gap, leading them to “make sense” of a concept. Here, we focus on adapting and applying sensemaking as a framework to analyze three groups of students working through a collaborative gas law activity. The activity was designed around the learning cycle to aid students in constructing the ideal gas law using an interactive simulation. For this analysis, we characterized student discourse using the structural components of the sensemaking epistemic game using a deductive coding scheme. Next, we further analyzed students’ epistemic form by assessing features of the activity and student discourse related to sensemaking: whether the question was framed in a real-world context, the extent of student engagement in robust explanation building, and analysis of written scientific explanations. Our work provides further insight regarding the application and use of the sensemaking framework for analyzing students’ problem solving by providing a framework for inferring the depth with which students engage in the process of sensemaking.

What Happens When We have Winter Heating of Our Rooms?

2020 ◽  
Vol 02 (01) ◽  
pp. 2020001
Author(s):  
Dulli C. Agrawal
Keyword(s):  
Internal Energy ◽  
Old Age ◽  
Ideal Gas ◽  
Van Der Waals Gas ◽  
Constant Weight ◽  
Gas Laws ◽  
Ideal Gas Law ◽  
Marginal Change ◽  
Three Stages ◽  
The Ideal

The illustrious question by German Astrophysicist R. Emden, “Why do we have winter heating?” has been re-examined for air following both the ideal and imperfect gas laws; the internal energy of the air in the room remains unaffected in the former case whereas it increases marginally for the latter one. The findings corresponding to ideal gas law were correlated by Emden with the mass of a person which does not change even though food is constantly consumed. This example corresponds to adulthood when the mass of a person remains more or less constant. But the marginal change of internal energy in the case of van der Waals gas is consistent with three stages of a person — initially a person grows during childhood followed by adulthood when he has more or less constant weight and finally in old age, it deteriorates.

Heat Transfer and Pressure Drop Through Nano-Fin Arrays in the Free-Molecular Flow Regime

2012 ◽  
Author(s):  
Michael James Martin
Keyword(s):  
Heat Transfer ◽  
Pressure Drop ◽  
Gas Flow ◽  
Ideal Gas ◽  
Molecular Flow ◽  
Ideal Gas Law ◽  
Transfer Equations ◽  
Flow Through ◽  
The One ◽  
The Ideal

Gas flow through arrays of rectangular nano-fins is modeled using the linearized free-molecular drag and heat transfer equations. These are combined with the one-dimensional equations for conservation of mass, momentum, and energy, and the ideal gas law, to find the governing equations for flow through the array. The results show that the pressure gradient, temperature, and local velocity of the gas are governed by coupled ordinary differential equations. The system of equations is solved for representative arrays of nano-fins to find the total heat transfer and pressure drop across a 1 cm chip.

Simple Predictions for the Sonic Conditions in a Real Gas

1977 ◽  
Vol 99 (1) ◽  
pp. 217-225 ◽  
Author(s):  
P. A. Thompson ◽  
D. A. Sullivan
Keyword(s):  
Equation Of State ◽  
Closed Form ◽  
Thermodynamic Parameters ◽  
Ideal Gas ◽  
Accurate Prediction ◽  
Bernoulli Equation ◽  
Real Gas ◽  
Similarity Principle ◽  
Isentropic Flow ◽  
The Ideal

The steady isentropic flow of a fluid which satisfies an arbitrary equation of state is treated, with emphasis on the prediction of pressure, density, velocity, and massflow at the sonic state. The isentrope P(v) is described by a limited number of thermodynamic parameters, the most important ones being the soundspeed c and fundamental derivative Γ. Using this description, an application of the Bernoulli equation and appropriate thermodynamic relations yields simple closed-form predictions for the sonic state. These predictions are recognizable as generalizations of well-known ideal gas formulas, but are applicable to fluids very far removed from the ideal gas state, even including liquids. Comparisons in several cases for which precise independent solutions are available suggest that the methods found here are accurate. A derived similarity principle allows the accurate prediction of sonic properties from any single given sonic property.

scholarly journals The Key to the Problem of Reversible Chemical Hydrogen Storage Is 12 kJ (mol H2)-1

2018 ◽  
Author(s):  
Roland Hermann Pawelke
Keyword(s):  
Hydrogen Storage ◽  
Ideal Gas ◽  
Solid Hydrogen ◽  
Hydrogen Sorption ◽  
Equilibrium Thermodynamics ◽  
Ideal Gas Law ◽  
Chemical Hydrogen Storage ◽  
The Ideal

This article outlines a simple theoretical formalism illuminating the boundaries to reversible solid hydrogen storage, based on the ideal gas law and classic equilibrium thermodynamics. A global picture of chemical reversible hydrogen sorption is unveiled, including a thermodynamic explanation of partial reversibility.<br>

scholarly journals An Ideal yet Highly Accurate Model Correlating Global Average Temperature to Excess CO2-Emissions

2021 ◽  
Author(s):  
Roland Hermann Pawelke
Keyword(s):  
Transition State Theory ◽  
Ideal Gas ◽  
State Theory ◽  
Average Temperature ◽  
Global Mean Temperature ◽  
Ideal Gas Law ◽  
System Temperature ◽  
First Time ◽  
Global Mean ◽  
The Ideal

The causality of preceding atmospheric excess-to-equilibrium CO<sub>2</sub>-amounts and trailing system temperature increase is captured in terms of the ideal gas law, equilibrium thermodynamics and transition state theory for the first time: the model’s performance is excellent, publicly available global mean temperature data from 1880 (13.58 °C / 290.7 ppm) to April 2021 (14.49 °C / 416.2 ppm) are reproduced at less than ±2 % deviation. Eight future global mean temperatures for atmospheric CO<sub>2</sub>-levels between 450 ppm and 7000 ppm are extrapolated and an empiric expression of the relation is derived. The model’s ideal nature allows adaption for other greenhouse gases and provides a reference for conclusions about the energetic weighting and the wider significance of the CO<sub>2</sub>-based proportion in the total Greenhouse effect.

scholarly journals The Master Key to the Problem of Reversible Chemical Hydrogen Storage is 12 kJ (mol H2)-1

2019 ◽  
Author(s):  
Roland Hermann Pawelke
Keyword(s):  
Energy Storage ◽  
Hydrogen Storage ◽  
Predictive Power ◽  
Storage Capacity ◽  
Reaction Pathway ◽  
Ideal Gas ◽  
Equilibrium Thermodynamics ◽  
Ideal Gas Law ◽  
Chemical Hydrogen Storage ◽  
The Ideal

<p>This article outlines a potent theoretical formalism illuminating the boundaries to reversible solid hydrogen storage based on the ideal gas law and classic equilibrium thermodynamics. A global picture of chemical reversible hydrogen sorption is unveiled including a thermodynamic explanation of partial reversibility. This is utilized to elucidate a multitude of issues from metal hydride chemistry: Highlights are why the substitution of a mere 4 mol % Na by K in Ti-doped NaAlH<sub>4</sub> raises the reversible storage capacity by 42 % and elaboration of the reaction pathway in (Rb/K)H-doped Mg(NH<sub>2</sub>)<sub>2</sub>/2LiH. The findings of this work allow for a change of paradigm towards the understanding of reversible chemical energy storage and provide a hitherto missing tool of ample analytic and predictive power, complementary to experiment.</p>

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