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A system of n non interacting classical point particles are constrained to move on the 2d surfaced sphere .the internal energy of system is A)3/2 NkT B)1/2 NkT C)NkT D)5/2 NkT?
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A system of n non interacting classical point particles are constraine...
Internal Energy of N non interacting classical point particles on a 2D sphere
Internal energy of a system of particles is given by the sum of kinetic and potential energies of all particles in the system.
1. Kinetic energy:
Since the particles are non-interacting, their kinetic energy is given by the translational kinetic energy of each particle.
On a 2D surface like a sphere, the kinetic energy of a particle is given by \( \frac{1}{2} m v^2 \).
Since the particles are classical, we can use the equipartition theorem which states that each degree of freedom contributes \(\frac{1}{2} kT\) to the energy, where k is the Boltzmann constant and T is the temperature.
In 2D, each particle has 2 degrees of freedom (for x and y directions), so the total kinetic energy for N particles is \( \frac{1}{2} NkT \).
2. Potential energy:
Since the particles are non-interacting, there is no potential energy contribution to the system.
Internal Energy:
Therefore, the internal energy of the system of N non-interacting classical point particles constrained to move on a 2D surface like a sphere is given by the kinetic energy, which is \( \frac{1}{2} NkT \).
Therefore, the correct option is:
A) \( \frac{3}{2} NkT \).
Internal energy of a system of particles is given by the sum of kinetic and potential energies of all particles in the system.
1. Kinetic energy:
Since the particles are non-interacting, their kinetic energy is given by the translational kinetic energy of each particle.
On a 2D surface like a sphere, the kinetic energy of a particle is given by \( \frac{1}{2} m v^2 \).
Since the particles are classical, we can use the equipartition theorem which states that each degree of freedom contributes \(\frac{1}{2} kT\) to the energy, where k is the Boltzmann constant and T is the temperature.
In 2D, each particle has 2 degrees of freedom (for x and y directions), so the total kinetic energy for N particles is \( \frac{1}{2} NkT \).
2. Potential energy:
Since the particles are non-interacting, there is no potential energy contribution to the system.
Internal Energy:
Therefore, the internal energy of the system of N non-interacting classical point particles constrained to move on a 2D surface like a sphere is given by the kinetic energy, which is \( \frac{1}{2} NkT \).
Therefore, the correct option is:
A) \( \frac{3}{2} NkT \).
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A system of n non interacting classical point particles are constrained to move on the 2d surfaced sphere .the internal energy of system is A)3/2 NkT B)1/2 NkT C)NkT D)5/2 NkT?
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A system of n non interacting classical point particles are constrained to move on the 2d surfaced sphere .the internal energy of system is A)3/2 NkT B)1/2 NkT C)NkT D)5/2 NkT? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A system of n non interacting classical point particles are constrained to move on the 2d surfaced sphere .the internal energy of system is A)3/2 NkT B)1/2 NkT C)NkT D)5/2 NkT? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A system of n non interacting classical point particles are constrained to move on the 2d surfaced sphere .the internal energy of system is A)3/2 NkT B)1/2 NkT C)NkT D)5/2 NkT?.
A system of n non interacting classical point particles are constrained to move on the 2d surfaced sphere .the internal energy of system is A)3/2 NkT B)1/2 NkT C)NkT D)5/2 NkT? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A system of n non interacting classical point particles are constrained to move on the 2d surfaced sphere .the internal energy of system is A)3/2 NkT B)1/2 NkT C)NkT D)5/2 NkT? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A system of n non interacting classical point particles are constrained to move on the 2d surfaced sphere .the internal energy of system is A)3/2 NkT B)1/2 NkT C)NkT D)5/2 NkT?.
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