Compared to solid and liquid properties, the properties of gases are simpler to comprehend. This is primarily due to the fact that molecules in a gas are dispersed widely apart and barely interact with one another unless they collide. The molecules that make up an ideal gas are those that have no external forces at work other than the forces created when they collide with the container wall and with each other.
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In this article, we will cover the concept of the Ideal gas equation. This concept is part of the chapter Kinetic Theory of Gases, which is a crucial chapter in Class 11 physics. It is not only essential for board exams but also for competitive exams like the Joint Entrance Examination (JEE Main), National Eligibility Entrance Test (NEET), and other entrance exams such as SRMJEE, BITSAT, WBJEE and more. Over the last ten years of the JEE Main exam (from 2013 to 2023), a total of twelve questions have been asked on this concept. And for NEET ten questions were asked from this concept.
Let's read this entire article to gain an in-depth understanding of the Ideal gas equation.
The equation which relates the pressure (P), volume (V) and temperature (T) of the given state of an ideal gas is known as an ideal gas equation or equation of state.
From Boyle’s law, we get
and From Charle’s Law, we get
And from Avogadro’s Law, we get
And from equation (1), (2), (3)
we can write
So, Ideal Gas Equation is given as
P V = n R T
where
T= Temperature
P= pressure of ideal gas
V= volume
n= numbers of mole
R = universal gas constant
Universal gas constant (R)
At S.T.P. the value of the universal gas constant is the same for all gases. And its value is given as
And its Dimension is :
It is represented by the per mole gas constant.
It is represented by per gram gas constant.
i.e.
It's unit is
Example 1: Which of the following shows the correct relationship between the pressure ‘P’ and density ρ of an ideal gas at constant temperature?
1)
2)
3)
4)
Solution:
Ideal gas equation
P V=n R T
wherein
T = Temperature
P= pressure of ideal gas
V= volume
n= numbers of mole
R = universal gas constant
For an ideal gas
Hence, the graph between
Hence, the answer is option (4).
Example 2: ‘ n’ moles of an ideal gas undergoes a process A→B as shown in the figure. The maximum temperature of the gas during the process will be :
1)
2)
3)
4)
Solution:
At any point between A & B, we can write a relation between P & V by using the equation of the straight-line
From the ideal gas equation
Hence, the answer is option option (1).
Example 3: One mole of an ideal monoatomic gas is taken along the path ABCA as shown in the PV diagram. The maximum temperature attained by the gas along the path BC is given by :
1)
2)
3)
4)
Solution:
Ideal gas equation
wherein
T= Temperature
P= pressure of ideal gas
V= volume
n= numbers of mole
R = universal gas constant
equation of the given path is
for T to be maximum
Hence, the answer is option (2)
Example 4: This is true for an ideal gas.
(1) Molecule of gas is identical spherical rigid and perfectly elastic point mass.
(2) There is always some attractive and repulsive force acting between gas molecules.
(3) The density of a gas is constant at all points of the container molecules
1) only 1
2) 1 and 3
3) 2 and 3
4) only 3
Solution:
For ideal gas
Hence, the answer is the option 2
Example 5: The temperature of an open room of volume 30
1) −1.61×1023
2) 1.38×1023
3) 2.5×1025
4) −2.5×1025
Solution:
change in the Number of molecules
Hence, the answer is the option (4).
Not all gases can be represented by the ideal gas equation; only ideal gases can. It cannot be used for gases that are exceptionally large, exhibit strong intermolecular forces, collide in an inelastic manner, or lack kinetic energy proportional to the ideal gas's absolute temperature. Thus, there are restrictions on the Ideal Gas Equation. Because the molecular mass and the intermolecular forces are important under these circumstances, it is ineffective at low temperatures, high densities, and extremely high pressures. Heavy gases, such as refrigerants, and gases with extremely high intermolecular forces, such as water vapour, cannot be treated with it.
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