Thermodynamics - Whcih isotherm has higher temperature?

In summary, the student is asking for help in identifying which of the two given isotherms is at a higher temperature, as the area of the rectangle formed by P and V seems to be equal for both curves. However, the answer in their book states that T1<T2. The teacher explains that on an ideal gas PV diagram, the temperature is greater at locations where the product of P and V is greater. The teacher also mentions that the area of the rectangle measures nRT and if n differs between the two gases, the temperatures may not be equal. The student expresses their gratitude for the help provided.
  • #1
Amith2006
427
2
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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  • #2
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.
 
  • #3
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
 
  • #4
Sir,
I don't have words to thank you. This is a service to all students like me.
 

1. What is an isotherm in thermodynamics?

An isotherm in thermodynamics is a line on a graph that connects points of equal temperature for a particular system. This means that all points on the isotherm have the same temperature, regardless of their other properties such as pressure or volume.

2. How do you determine which isotherm has a higher temperature?

The isotherm with a steeper slope on a temperature vs. volume graph will have a higher temperature. This is because a steeper slope indicates a greater change in temperature for a given change in volume.

3. What is the relationship between isotherms and thermal equilibrium?

In thermodynamics, thermal equilibrium refers to a state where there is no net flow of heat between two systems. Isotherms are important in determining thermal equilibrium because they represent a constant temperature and can help identify when two systems have reached the same temperature.

4. Can two isotherms intersect?

No, two isotherms cannot intersect on a temperature vs. volume graph. This is because each isotherm represents a unique temperature, and two different temperatures cannot exist at the same point.

5. How does the shape of an isotherm relate to the properties of a substance?

The shape of an isotherm can provide information about the properties of a substance. For example, a convex (upward-curving) isotherm indicates that the substance has a positive coefficient of thermal expansion, while a concave (downward-curving) isotherm indicates a negative coefficient of thermal expansion.

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