Thermodynamics - Whcih isotherm has higher temperature?

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SUMMARY

The discussion centers on identifying which isotherm represents a higher temperature in a P-V diagram for ideal gases. It is established that the area of the rectangle formed by pressure (P) and volume (V) is equal for both isotherms, leading to initial confusion regarding temperature equality. However, the conclusion is that if the number of moles (n) differs between the gases, the temperatures are not equal, confirming that T1 is less than T2 when the area is the same. The relationship between the product of P and V and temperature is critical in determining the higher temperature isotherm.

PREREQUISITES
  • Understanding of ideal gas laws and equations, specifically PV = nRT
  • Familiarity with P-V diagrams and isotherms in thermodynamics
  • Knowledge of the concept of moles in gas calculations
  • Basic principles of thermodynamic temperature scales
NEXT STEPS
  • Study the implications of the ideal gas law on thermodynamic processes
  • Learn how to interpret P-V diagrams for various thermodynamic processes
  • Explore the relationship between pressure, volume, and temperature in real gases
  • Investigate the concept of isothermal processes and their applications in engineering
USEFUL FOR

Students of thermodynamics, physics enthusiasts, and professionals in engineering fields who require a deeper understanding of gas behavior and thermodynamic principles.

Amith2006
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Sir,
Two isotherms are given. How do we identify which one is at higher temperature? The area of the rectangle formed with P & V as sides seems to equal for both the curves. So I think the temperatures are equal. But the answer given in my book is T1<T2.
I am herewith attaching the P-V diagram.
 

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I can't see the attachment yet, but the temperature is greater on an ideal gas PV diagram at the locations where the product of P*V is greater. This means that as go up-and-right on the PV diagram, you will increase in temperature.
 
Amith2006 said:
Sir,
Two isotherms are given. How do we identify which one is at higher temperature? The area of the rectangle formed with P & V as sides seems to equal for both the curves. So I think the temperatures are equal. But the answer given in my book is T1<T2.
I am herewith attaching the P-V diagram.
I can't see your diagram yet but note: the area of the rectangle of sides P and V measures (PV =) nRT. If n differs between the two gases, the PV area might be the same but the temperatures are not.

AM
 
Sir,
I don't have words to thank you. This is a service to all students like me.
 

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