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A system of N non-interacting classical point particles is constrained to move on the two-dimensional surface of a sphere. The internal energy of the system is in units of NkBT?
Correct answer is '1'. Can you explain this answer?
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Verified Answer
A system of N non-interacting classical point particles is constrained...
Since the particle is moving on two dimensional surface, its degree of freedom = 2.
Hence, for N non-interacting particles total degree of freedom = 2N
The energy per degree of freedom = 1/2 kBT
Hence, total energy
U = NkBT
The correct answer is: 1
Hence, for N non-interacting particles total degree of freedom = 2N
The energy per degree of freedom = 1/2 kBT
Hence, total energy
U = NkBT
The correct answer is: 1
Most Upvoted Answer
A system of N non-interacting classical point particles is constrained...
Introduction:
In this system, N non-interacting classical point particles are confined to move on the two-dimensional surface of a sphere. We need to determine the units of the internal energy of the system, which is given in terms of NkBT.
Explanation:
To understand the units of the internal energy, let's break down the given expression NkBT.
N:
N represents the number of particles in the system. It is a dimensionless quantity since it is simply counting the number of particles. Therefore, it does not have any units associated with it.
k:
k is the Boltzmann constant, which relates temperature to energy. It has units of energy per temperature, usually expressed as J/K (Joules per Kelvin).
T:
T represents temperature and is measured in Kelvin. Temperature is a measure of the average kinetic energy of particles in a system.
Combining the terms:
Multiplying N (dimensionless) with k (units of energy per temperature) gives us units of energy. So, the product Nk has units of energy.
Multiplying Nk with T (temperature in Kelvin) gives us the units of the internal energy of the system, NkBT.
Conclusion:
The units of the internal energy of the system, in terms of NkBT, are energy units (Joules, for example). Therefore, the correct answer is '1'.
In this system, N non-interacting classical point particles are confined to move on the two-dimensional surface of a sphere. We need to determine the units of the internal energy of the system, which is given in terms of NkBT.
Explanation:
To understand the units of the internal energy, let's break down the given expression NkBT.
N:
N represents the number of particles in the system. It is a dimensionless quantity since it is simply counting the number of particles. Therefore, it does not have any units associated with it.
k:
k is the Boltzmann constant, which relates temperature to energy. It has units of energy per temperature, usually expressed as J/K (Joules per Kelvin).
T:
T represents temperature and is measured in Kelvin. Temperature is a measure of the average kinetic energy of particles in a system.
Combining the terms:
Multiplying N (dimensionless) with k (units of energy per temperature) gives us units of energy. So, the product Nk has units of energy.
Multiplying Nk with T (temperature in Kelvin) gives us the units of the internal energy of the system, NkBT.
Conclusion:
The units of the internal energy of the system, in terms of NkBT, are energy units (Joules, for example). Therefore, the correct answer is '1'.
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A system of N non-interacting classical point particles is constrained to move on the two-dimensional surface of a sphere. The internal energy of the system is in units of NkBT?Correct answer is '1'. Can you explain this answer?
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A system of N non-interacting classical point particles is constrained to move on the two-dimensional surface of a sphere. The internal energy of the system is in units of NkBT?Correct answer is '1'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A system of N non-interacting classical point particles is constrained to move on the two-dimensional surface of a sphere. The internal energy of the system is in units of NkBT?Correct answer is '1'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A system of N non-interacting classical point particles is constrained to move on the two-dimensional surface of a sphere. The internal energy of the system is in units of NkBT?Correct answer is '1'. Can you explain this answer?.
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