Ideal Gas Behavior: Choose the Right Diagram

In summary, the conversation discusses the behavior of an ideal gas and how to determine it from various graphs. The equation PV = nRT is introduced and its relationship to the graphs is explained. It is concluded that diagram C is the most accurate representation of an ideal gas's behavior.
  • #1
b_andries
13
0
Hi guys,

Can someone explain me please how to find the following question?
Which diagram represents the behavior of an ideal gas the most?

attachment.php?attachmentid=35606&d=1305538124.jpg


I know it's C but I don't know why. They all seem to represent the behavior of a ideal gas.
But why C mor than the others?

Thanks
 

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  • #2
What is the equation that relates P, V and T for an ideal gas?

What is the relationship between P and T if V is constant (first graph)?

What is the relationship between V and T if P is constant (second graph)?

What is the relationship between P and 1/V if T is constant (third graph)?

AM
 
  • #3
What is the equation that relates P, V and T for an ideal gas?

P.V = n.R.T

What is the relationship between P and T if V is constant (first graph)?
==>T instead of V is constant here no(same values on x-axis)?

P.V = n.R. = constant so this should be wrong because there is a slope

What is the relationship between V and T if P is constant (second graph)?
isn't here also T constant instead of P?

V = n.R /P
So if V rises than P has to decline
This graph would not be possible because T is constant and P and V both rise.What is the relationship between P and 1/V if T is constant (third graph)?

Volume here is constant(same values on x-axis)
P= n.R.T (So if P rises T has to Rise too)
In this case they both rise so it would also be possible
 
  • #4
b_andries said:
What is the equation that relates P, V and T for an ideal gas?

P.V = n.R.T
You don't need the .'s. Just: PV = nRT
What is the relationship between P and T if V is constant (first graph)?
==>T instead of V is constant here no(same values on x-axis)?
No. P is on the y-axis and T is on the x axis. Each line represents the points (P,T) for which V has the same value (that value is stated at the end of the line).

What is the relationship between V and T if P is constant (second graph)?
isn't here also T constant instead of P?
No. V is on the y-axis and T is on the x axis. Each line represents the points (V,T) for which P has the same value (that value is stated at the end of the line).

What is the relationship between P and 1/V if T is constant (third graph)?

Volume here is constant(same values on x-axis)
No. P is on the y-axis and 1/V is on the x axis. Each line represents the points (P,1/V) for which T has the same value (that value is stated at the end of the line).

AM
 
  • #5
Ok thanks,

Now i know what I've done wrong
 
  • #6
b_andries said:
Ok thanks,

Now i know what I've done wrong
Can you explain why c) is the correct answer (and why a) and b) do not fit: PV=nRT?)

AM
 
  • #7
P(1/V)= nRT 1/V (function P with respect to 1/V)
So here nRT represents the slope of the graph
A larger Temperature gives a larger slope, which is what diagram C shows
So diagram C is correct.


P(T) = nR/V T(function P with respect to T)
So nR/V represents the slope of the graph
A Larger volume should give smaller slope, but in diagram A, larger V gives larger slope.
So diagram A is wrong.


V(T) = nR/P T(function V with respect to T)
So nR/P represents the slope of the graph
A Larger Pressure should give a smaller slope, but in diagram B, larger Pressure gives a larger slope.
Thus diagram B is wrong.

Am I correct?
 
  • #8
b_andries said:
P(1/V)= nRT 1/V (function P with respect to 1/V)
So here nRT represents the slope of the graph
A larger Temperature gives a larger slope, which is what diagram C shows
So diagram C is correct.


P(T) = nR/V T(function P with respect to T)
So nR/V represents the slope of the graph
A Larger volume should give smaller slope, but in diagram A, larger V gives larger slope.
So diagram A is wrong.


V(T) = nR/P T(function V with respect to T)
So nR/P represents the slope of the graph
A Larger Pressure should give a smaller slope, but in diagram B, larger Pressure gives a larger slope.
Thus diagram B is wrong.

Am I correct?
Yes. Very well explained.

AM
 

What is ideal gas behavior?

Ideal gas behavior is a concept in thermodynamics that describes the behavior of gases under certain conditions. It assumes that the gas particles have no volume, do not interact with each other, and are in constant, random motion. This behavior is often used as a simplified model to understand the properties of real gases.

What are the characteristics of an ideal gas?

An ideal gas has the following characteristics:

  • Particles have no volume
  • Particles do not interact with each other
  • Particles are in constant, random motion
  • Pressure is directly proportional to temperature at constant volume
  • Volume is directly proportional to temperature at constant pressure
  • No intermolecular forces
  • No phase transition

What is the ideal gas law?

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

What is the difference between real and ideal gases?

Real gases differ from ideal gases in that they do have volume and interact with each other. This means that at high pressures or low temperatures, real gases deviate from ideal gas behavior. Real gases also exhibit phase transitions, such as condensation and evaporation, which are not observed in ideal gases.

How do you choose the right diagram for ideal gas behavior?

The right diagram for ideal gas behavior is usually a pressure-volume (PV) or volume-temperature (VT) graph. These diagrams can be used to visualize the relationship between the variables in the ideal gas law. Additionally, these diagrams can also show the deviation of real gases from ideal gas behavior at different temperatures and pressures.

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