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Question

Give the dimensional formula for Boltzmann’s constant.


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Solution

Boltzmann's constant:

  1. Boltzmann constant is a proportionality constant that connects the average kinetic energy of a system with its absolute temperature.
  2. The exact value of the Boltzmann constant is 1.380649×10-23m2kgs-2K-1.
  3. For example, for an ideal gas mv22=32KT , where mv22=averagekineticenergyofmolecule.
  4. Boltzmann's constant, kB=2Ek3T.
  5. The dimensional formula for energy is mv22=M1L2T-2asv=L1T-1.
  6. kB=2Ek3T=M1L2T-2K=M1L2T-2K-1
  7. Hence, the dimensional formula of the Boltzmann constant is M1L2T-2K-1, Here, M implies dimension of mass, L implies length, T implies time, K implies temperature.

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