Are these two equations for adiabatic processes the same

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However, the two equations are equivalent and AMy is advised to double check her calculations. In summary, AMy is questioning two equations for temperature change and is advised to double check her calculations as the equations are equivalent.
  • #1
Rujano
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Hi.

I was just wondering about this because is most texts I've seen this one:

Tf/Ti = (Vi/Vf)^y - 1

y= gamma (Cp/CV)

However, in my worksheets I always see this one:

Tf/Ti = (Vf/Vi)^1 -y

And actually, when I tried to solve one problem, I tried to use the first one but the result wasn't the same...
 
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  • #2
Rujano said:
Hi.

I was just wondering about this because is most texts I've seen this one:

Tf/Ti = (Vi/Vf)^y - 1

y= gamma (Cp/CV)

However, in my worksheets I always see this one:

Tf/Ti = (Vf/Vi)^1 -y

And actually, when I tried to solve one problem, I tried to use the first one but the result wasn't the same...
The two expressions are equivalent:

[tex]x^y = x^{({-1}*{-y})} = (1/x)^{-y}[/tex]

So I suggest that you go back and check your math again. The result has to be the same.

AM
 

FAQ: Are these two equations for adiabatic processes the same

What is an adiabatic process?

An adiabatic process is a thermodynamic process in which there is no transfer of heat or mass between a system and its surroundings. This means that the system is isolated and there is no external energy input.

How do you determine if two equations for adiabatic processes are the same?

To determine if two equations for adiabatic processes are the same, you can compare the mathematical forms of the equations and check if they have the same variables and constants. Additionally, you can solve both equations for the same variables and see if they yield the same result.

What are the key differences between these two equations for adiabatic processes?

The key differences between these two equations for adiabatic processes may be in the assumptions made about the system and the variables used. Some equations may only apply to ideal gas systems, while others may apply to more general systems. Additionally, the equations may differ in terms of the constants used and the level of accuracy.

Can these two equations for adiabatic processes be used interchangeably?

It depends on the specific situation and the level of accuracy needed. If the assumptions and variables of the equations are the same, then they can likely be used interchangeably. However, it is always best to check for consistency and accuracy when using any equations in scientific calculations.

How are adiabatic processes used in real-world applications?

Adiabatic processes are commonly used in various industries, such as in the design of heat engines and refrigeration systems. They are also important in atmospheric and oceanic science for understanding and predicting weather patterns. Additionally, adiabatic processes play a role in the study of chemical reactions and in the design of industrial processes.

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