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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...
    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
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    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'.
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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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