Question

Q. Deduce dimensional formulae of
(i) Boltzmann's constant
(ii) Mechanical equivalent of heat.​

Answer 1

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QUESTION:

Deduce dimensional formulae of

(i) Boltzmann's constant

(ii) Mechanical equivalent of heat.​

Answer:

1.Boltzmann's constant

The Boltzmann constant (kB or k), which is named after Ludwig Boltzmann, is a physical constant relating the average kinetic energy of particles in a gas with the temperature of the gas.It is the gas constant R divided by the Avogadro constant Na:

k= R/Na [Na is Avogadro number]

The Boltzmann constant has the dimension energy divided by temperature, the same as entropy.

as we know that pV=nRT.

where R is the gas constant (8.3144598(48) J/K/mol

Introducing the Boltzmann constant transforms the ideal gas law into an alternative form:

pV=NkT

where N is the number of molecules of gas. For n = 1 mol, N is equal to the number of particles in one mole (Avogadro's number).

The dimensional formula for Boltzmann’s constant is

ML²T⁻²θ⁻¹

2.Mechanical equivalent of heat

Mechanical equivalent of heat can be defined as the amount of work done to produce a unit quantity of heat. In other words whenever a mechanical work is completely transformed into heat, the amount of heat produced is directly proportional to the amount of work done.

W ∝ Q  —— Where W = Amount of Work and Q = units of heat.

W = J Q

In the above equation constant J is Known as Mechanical equivalent of heat or Joule’s equivalent.

From above equation we get,

Mechanical equivalent of heat (J) = Amount of Work (W) / units of Heat (Q).

Dimensional Formula of Work = M1L2T-2

Dimensional Formula of Heat = M1L2T-2

substituting these values we get,

Dimensional Formula of Mechanical equivalent of heat (J) = M0L0T-0 . we can also say Mechanical equivalent of heat (J) is dimensionless quantity.

SI unit of Mechanical equivalent of heat (J) is Joules/calorie (J calorie-1 )

#BE_BRAINLY

#RISHI

Answer 2

Explanation:

I. ML^2T^-2K^-1.

ii. M^0L^0T^0.

basically mechanical equivalent of heat is dimension less quantity.

M =mass

L=length or distance

T=time

K=temperature.

hope it will help you.

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