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According to the law of equipartition of energy if the absolute temperature of water is T, then the energy of water molecule is equal to the: (kB = Boltzmann constant and R = Universal gas constant)

According to the law of equipartition of energy if the absolute temperature of water is T, then the energy of water molecule is equal to the: (kB = Boltzmann constant and R = Universal gas constant) Correct Answer 9k<sub>B</sub>T

CONCEPT:

Specific heat capacity of water:

  • We can use the law of equipartition of energy to determine the specific heat of the water.
  • We treat water like a solid.
  • We consider every atom vibrating about its mean position. So the average energy of each atom is given as,

⇒ E = 3kBT

  • The water molecule has three atoms, two hydrogens, and one oxygen.
  • So the energy of one molecule of water is given as,

⇒ Ew = 9kBT

  • If NA is the number of molecules in one mole of water, then the average energy of one mole of water is given as,

⇒ U = 9NAkBT = 9RT

Where kB = Boltzmann constant, T = absolute temperature, and R = universal gas constant

  • So the molar specific heat of water is given as,

⇒ C = 9R

  • This is the value observed and the agreement is very good.
  • In the calorie, gram, degree units, water is defined to have unit-specific heat.
  • The predicted specific heats are independent of temperature.

EXPLANATION:

  • According to the law of equipartition of energy, the energy of one molecule of water is given as,

⇒ Ew = 9kBT

  • Hence, option 2 is correct.

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Read the passage carefully and select the best answer to each question out of the given four alternatives.
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