Answer
64.8k+ views
Hint: Internal energy is the sum of the kinetic and potential energies of a particle. As the particles in an ideal gas do not interact, the system has no potential energy. So the internal energy of an ideal gas is, therefore, the sum of the kinetic energies of the particles in the gas.
Formulae used:
$E = \dfrac{3}{2}PV$
Where $E$ is the energy of the ideal gas, $P$ is the pressure of the ideal gas and $V$ is the volume of the ideal gas.
Complete step by step answer:
In the question, the volume of the ideal gas is given as
$ \Rightarrow V = 2{m^3}$
And the pressure of the ideal gas is
$ \Rightarrow P = 3 \times {10^6}pa$
As $1pa = 1\dfrac{N}{{{m^2}}}$
So the pressure becomes
$ \Rightarrow P = 3 \times {10^6}\dfrac{N}{{{m^2}}}$
For any idea gas, the energy is given by,
$ \Rightarrow E = \dfrac{3}{2}PV$
Where $E$ is the energy of the ideal gas, $P$ is the pressure of the ideal gas and $V$ is the volume of the ideal gas.
Substituting the values of $P$ and $V$ we get,
$ \Rightarrow E = 9 \times {10^6}J$
So the answer is an option (D).
Additional Information: An ideal gas is a theoretical gas made up of many atoms that is not subject to interparticle interactions. The ideal gas concept is useful because it obeys the ideal gas law. At standard temperature and pressure conditions, most real gases behave like an ideal gas. Many gases such as nitrogen, oxygen, hydrogen, noble gases, and some heavier gases like carbon dioxide can be treated as ideal gases within some limits. Generally, a gas behaves more like an ideal gas at a higher temperature and lower pressure, as the potential energy due to intermolecular forces becomes less significant compared with the particles' kinetic energy, and the size of the molecules becomes less significant compared to the empty space between them.
Note: While solving this question, be careful with the units of the terms. All the units of all the terms should be in the same system otherwise the calculated answers can be incorrect.
Formulae used:
$E = \dfrac{3}{2}PV$
Where $E$ is the energy of the ideal gas, $P$ is the pressure of the ideal gas and $V$ is the volume of the ideal gas.
Complete step by step answer:
In the question, the volume of the ideal gas is given as
$ \Rightarrow V = 2{m^3}$
And the pressure of the ideal gas is
$ \Rightarrow P = 3 \times {10^6}pa$
As $1pa = 1\dfrac{N}{{{m^2}}}$
So the pressure becomes
$ \Rightarrow P = 3 \times {10^6}\dfrac{N}{{{m^2}}}$
For any idea gas, the energy is given by,
$ \Rightarrow E = \dfrac{3}{2}PV$
Where $E$ is the energy of the ideal gas, $P$ is the pressure of the ideal gas and $V$ is the volume of the ideal gas.
Substituting the values of $P$ and $V$ we get,
$ \Rightarrow E = 9 \times {10^6}J$
So the answer is an option (D).
Additional Information: An ideal gas is a theoretical gas made up of many atoms that is not subject to interparticle interactions. The ideal gas concept is useful because it obeys the ideal gas law. At standard temperature and pressure conditions, most real gases behave like an ideal gas. Many gases such as nitrogen, oxygen, hydrogen, noble gases, and some heavier gases like carbon dioxide can be treated as ideal gases within some limits. Generally, a gas behaves more like an ideal gas at a higher temperature and lower pressure, as the potential energy due to intermolecular forces becomes less significant compared with the particles' kinetic energy, and the size of the molecules becomes less significant compared to the empty space between them.
Note: While solving this question, be careful with the units of the terms. All the units of all the terms should be in the same system otherwise the calculated answers can be incorrect.
Recently Updated Pages
Write a composition in approximately 450 500 words class 10 english JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Arrange the sentences P Q R between S1 and S5 such class 10 english JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
What is the common property of the oxides CONO and class 10 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
What happens when dilute hydrochloric acid is added class 10 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
If four points A63B 35C4 2 and Dx3x are given in such class 10 maths JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
The area of square inscribed in a circle of diameter class 10 maths JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Other Pages
Excluding stoppages the speed of a bus is 54 kmph and class 11 maths JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
In the ground state an element has 13 electrons in class 11 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Electric field due to uniformly charged sphere class 12 physics JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
A boat takes 2 hours to go 8 km and come back to a class 11 physics JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
According to classical free electron theory A There class 11 physics JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)