Answer
Verified
38.1k+ views
Hint: It is a proportionality factor that relates average kinetic energy of particles in gas with thermodynamic temperature of gas.
Complete step by step solution:
It is known that Boltzmann constant ($k_b$), is a physical constant relating the average kinetic energy of particles in a gas with the temperature of the gas.
It is sort of a conversion type.
For simple ideal gases whose molecules are of mass m and have only kinetic energy, the Boltzmann constant k relates the average kinetic energy per molecule to the absolute temperature. The relationship can be given by: $\dfrac{{m{v^2}}}{2} = \dfrac{3}{2}kT$ where ${v^2}$ is the average of the squared velocity of gas molecules and $T$is the absolute temperature(in kelvin).
Also, it is the gas constant R divided by the Avogadro number NA : ${K_b} = \dfrac{R}{{{N_A}}}$.
Now we can calculate the value of Kb by using the formula: ${K_b} = \dfrac{R}{{{N_A}}}$
Calculation:
We know value of gas constant, $R = 8.3144J/K/mol$
Also, value of Avogadro number, ${N_A} = 6.02214 \times {10^{23}}$
Therefore, Boltzmann constant, ${K_b} = \dfrac{R}{{{N_A}}} = \dfrac{{8.3144}}{{6.02214 \times {{10}^{23}}}} = 1.3806 \times {10^{ - 23}}$ J/K/molecule
Now to convert the above calculated value of $K_b$ from J/K/molecule to erg $K^{-1}$ molecul$e^{-1}$, we have to multiply the above calculated value by 107:
${k_b} = \left( {1.3806 \times {{10}^{ - 23}}} \right)\left( {{{10}^7}} \right) = 1.3806 \times {10^{ - 16}}$ erg $K^{-1}$ molecul$e^{-1}$.
Hence, from above points we can now easily conclude that option A is the correct option.
Note: It should be remembered that Boltzmann constant is measured by measuring atomic speed of gas or speed of sound of gas. Also, one should remember the dimensional formula for Boltzmann’s constant which is ${M^2}{L^2}{T^{ - 2}}{\theta ^{ - 1}}$.
Complete step by step solution:
It is known that Boltzmann constant ($k_b$), is a physical constant relating the average kinetic energy of particles in a gas with the temperature of the gas.
It is sort of a conversion type.
For simple ideal gases whose molecules are of mass m and have only kinetic energy, the Boltzmann constant k relates the average kinetic energy per molecule to the absolute temperature. The relationship can be given by: $\dfrac{{m{v^2}}}{2} = \dfrac{3}{2}kT$ where ${v^2}$ is the average of the squared velocity of gas molecules and $T$is the absolute temperature(in kelvin).
Also, it is the gas constant R divided by the Avogadro number NA : ${K_b} = \dfrac{R}{{{N_A}}}$.
Now we can calculate the value of Kb by using the formula: ${K_b} = \dfrac{R}{{{N_A}}}$
Calculation:
We know value of gas constant, $R = 8.3144J/K/mol$
Also, value of Avogadro number, ${N_A} = 6.02214 \times {10^{23}}$
Therefore, Boltzmann constant, ${K_b} = \dfrac{R}{{{N_A}}} = \dfrac{{8.3144}}{{6.02214 \times {{10}^{23}}}} = 1.3806 \times {10^{ - 23}}$ J/K/molecule
Now to convert the above calculated value of $K_b$ from J/K/molecule to erg $K^{-1}$ molecul$e^{-1}$, we have to multiply the above calculated value by 107:
${k_b} = \left( {1.3806 \times {{10}^{ - 23}}} \right)\left( {{{10}^7}} \right) = 1.3806 \times {10^{ - 16}}$ erg $K^{-1}$ molecul$e^{-1}$.
Hence, from above points we can now easily conclude that option A is the correct option.
Note: It should be remembered that Boltzmann constant is measured by measuring atomic speed of gas or speed of sound of gas. Also, one should remember the dimensional formula for Boltzmann’s constant which is ${M^2}{L^2}{T^{ - 2}}{\theta ^{ - 1}}$.
Recently Updated Pages
To get a maximum current in an external resistance class 1 physics JEE_Main
If a wire of resistance R is stretched to double of class 12 physics JEE_Main
Let f be a twice differentiable such that fleft x rightfleft class 11 maths JEE_Main
Find the points of intersection of the tangents at class 11 maths JEE_Main
For the two circles x2+y216 and x2+y22y0 there isare class 11 maths JEE_Main
The path difference between two waves for constructive class 11 physics JEE_MAIN
Other Pages
A point charge q placed at the point A is A In stable class 12 physics JEE_Main
The mole fraction of the solute in a 1 molal aqueous class 11 chemistry JEE_Main
How many grams of concentrated nitric acid solution class 11 chemistry JEE_Main
Differentiate between homogeneous and heterogeneous class 12 chemistry JEE_Main
Dissolving 120g of urea molwt60 in 1000g of water gave class 11 chemistry JEE_Main
Electric field due to uniformly charged sphere class 12 physics JEE_Main