Isothermal Processes: Ideal Gas Equation and Doubts Explained

In summary: In my judgment as an experienced engineer, I see very little value in your spending your valuable time speculating about esoteric things like this. Your time would much better be served getting practice solving thermodynamics problems.
  • #1
mech-eng
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I have become almost sure but have only some small doubts. Are all isothermal process actually ideal gas equation PV=mRT? If all such processes are occur in closed systems, this is so. Because it is isothermal the temperature is constant, R is constant and so is mass for a closed system. So the left side of the equation should be PV, which is a polytropic process with n=1. But my doubts comes from that in books PV=mRT is always called ideal gas equation, not a polytropic process with n=1 and when it comes to a isothermal process they use ideal gas equation.

Thank you.
 
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  • #2
mech-eng said:
I have become almost sure but have only some small doubts. Are all isothermal process actually ideal gas equation PV=mRT? If all such processes are occur in closed systems, this is so. Because it is isothermal the temperature is constant, R is constant and so is mass for a closed system. So the left side of the equation should be PV, which is a polytropic process with n=1. But my doubts comes from that in books PV=mRT is always called ideal gas equation, not a polytropic process with n=1 and when it comes to a isothermal process they use ideal gas equation.

Thank you.
Real gases do not exactly obey the ideal gas law. And solids and liquids definitely do not obey the ideal gas law.

Also, in irreversible processes, even though the outer boundary of the gas may be held at constant temperature, the temperature is not constant throughout the body of the gas, and varies with spatial position and time. However, some would regard this as an isothermal process.
 
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  • #3
Chestermiller said:
Real gases do not exactly obey the ideal gas law. And solids and liquids definitely do not obey the ideal gas law.

Also, in irreversible processes, even though the outer boundary of the gas may be held at constant temperature, the temperature is not constant throughout the body of the gas, and varies with spatial position and time. However, some would regard this as an isothermal process.

What I meant to ask is neither for reals gases, nor if is there any real isothermal process. In this link second question is both related to ideal gas and its being a polytropic process. The second question in the link directly uses ideal gas equation as a polytropic process. So are all polytropic processes actually ideal gas equation?

http://home.iitk.ac.in/~suller/lectures/lec5.htm

Thank you very much.
 
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  • #4
mech-eng said:
What I meant to ask is neither for reals gases, nor if is there any real isothermal process. In this link second question is both related to ideal gas and its being a polytropic process. The second question in the link directly uses ideal gas equation as a polytropic process. So are all polytropic processes actually ideal gas equation?

http://home.iitk.ac.in/~suller/lectures/lec5.htm

Thank you very much.
Sorry. I don't understand your question. In the 2nd problem, they are analyzing the isothermal reversible expansion of an ideal gas. If the question is, "for a constant temperature reversible expansion, is it possible to satisfy an polytropic equation for a real gas, or does it have to be an ideal gas?", I think the answer is that it has to be an ideal gas.
 
  • #5
Chestermiller said:
Sorry. I don't understand your question. In the 2nd problem, they are analyzing the isothermal reversible expansion of an ideal gas. If the question is, "for a constant temperature reversible expansion, is it possible to satisfy an polytropic equation for a real gas, or does it have to be an ideal gas?", I think the answer is that it has to be an ideal gas.

1. Can there be any polytropic process with the indice equals to 1 which is described by an equation right hand side is not mRT?

2. Can there be any isothermal polytropic process having an indice other than 1?

I hope I am clear enough now.

Thank you.
 
  • #6
mech-eng said:
1. Can there be any polytropic process with the indice equals to 1 which is described by an equation right hand side is not mRT?

2. Can there be any isothermal polytropic process having an indice other than 1?

I hope I am clear enough now.

Thank you.
In my judgment as an experienced engineer, I see very little value in your spending your valuable time speculating about esoteric things like this. Your time would much better be served getting practice solving thermodynamics problems.
 

1. What is an isothermal process?

An isothermal process is a thermodynamic process in which the temperature of a system remains constant. This means that the internal energy of the system also remains constant, making it an ideal process to study the relationship between pressure, volume, and temperature.

2. What is the ideal gas equation?

The ideal gas equation, also known as the ideal gas law, is a mathematical relationship between the pressure, volume, and temperature of an ideal gas. It is expressed as PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin.

3. How is the ideal gas equation derived?

The ideal gas equation can be derived from the kinetic theory of gases, which states that the average kinetic energy of gas molecules is directly proportional to the temperature of the gas. This is combined with Boyle's Law, Charles' Law, and Avogadro's Law to form the ideal gas equation.

4. Can the ideal gas equation be applied to real gases?

While the ideal gas equation is a good approximation for most gases under normal conditions, it does not account for intermolecular forces and the volume of gas molecules. At high pressures or low temperatures, real gases deviate from ideal behavior, and more complex equations, such as the van der Waals equation, must be used.

5. What are some practical applications of understanding isothermal processes and the ideal gas equation?

Understanding isothermal processes and the ideal gas equation is crucial in various fields, including chemistry, physics, and engineering. It is used to predict the behavior of gases in different conditions, such as in the design of gas storage tanks or in industrial processes. It also serves as the basis for gas law calculations, which are useful for solving problems in many scientific and industrial settings.

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