Physics 11th Chap 8 : Topic 4 - Maryam Publications

Physics Chapter 8 : Topic 4

Boltzmann Constant

1 / 29

The Boltzmann constant $\mathbf{(k)}$ is related to the universal gas constant $\mathbf{(R)}$ by:

A) $\mathbf{k =}$ $\frac{\mathbf{N}_{\mathbf{A}}}{\mathbf{R}}$

B) $\mathbf{k =}$ $\frac{\mathbf{R}}{\mathbf{N}_{\mathbf{A}}}$

C) $\mathbf{k =}\mathbf{RN}_{\mathbf{A}}^{\mathbf{2}}$

D) $\mathbf{k\ = \ }\mathbf{RN}_{\mathbf{A}}$

2 / 29

In the expression $\mathbf{k}\mathbf{=}$ $\frac{\mathbf{R}}{\mathbf{N}_{\mathbf{A}}}$, $\mathbf{N}_{\mathbf{A}}\mathbf{\ }$represents:

A) Number of moles

B) Number of atoms in a molecule

C) Number of neutrons

D) Avogadro’s number

3 / 29

The value of the Boltzmann constant is approximately:

A) $\mathbf{1.38 \times}\mathbf{10}^{\mathbf{- 23}}\mathbf{\ J\ }\mathbf{K}^{\mathbf{- 1}}$

B) $\mathbf{8.31\ J\ mol}^{\mathbf{- 1\ }}\mathbf{K}^{\mathbf{- 1}}$

C) $\mathbf{9.8\ }\mathbf{N\ kg}^{\mathbf{- 1}}$

D) $\mathbf{6.02 \times}\mathbf{10}^{\mathbf{23}}$

4 / 29

The SI unit of the Boltzmann constant is:

A) $\mathbf{Nm}^{\mathbf{- 2}}$

B) $\mathbf{J\ mol}^{\mathbf{- 1}}$

C) $\mathbf{JK}^{\mathbf{- 1}}$

D) $\mathbf{J\ mol}^{\mathbf{- 1\ }}\mathbf{K}^{\mathbf{- 1}}$

5 / 29

The universal gas constant $\mathbf{(R)}$ has SI unit:

A) $\mathbf{N\ mol}^{\mathbf{- 1}}$

B) $\mathbf{JK}^{\mathbf{- 1}}$

C) $\mathbf{Pa\ m}^{\mathbf{- 3}}$

D) $\mathbf{J\ mol}^{\mathbf{- 1\ }}\mathbf{K}^{\mathbf{- 1}}$

6 / 29

The difference between $\mathbf{(R)}$ and $\mathbf{(k)}$ is that:

A) $\mathbf{(R)}$ applies per molecule and $\mathbf{(k)}$ per mole

B) $\mathbf{(R)}$ applies per mole and $\mathbf{(k)}$ per molecule

C) Both apply per mole only

D) Both have identical units

7 / 29

Which quantity connects macroscopic gas behavior to molecular behavior?

A) Boltzmann constant

B) Volume

C) Density

D) Pressure

8 / 29

If $\mathbf{R = 8.31\ J\ }\mathbf{mol}^{\mathbf{- 1}}\mathbf{K}^{\mathbf{- 1}}$ and $\mathbf{N}_{\mathbf{A}}\mathbf{= 6.02 \times}\mathbf{10}^{\mathbf{23}}$, then $\mathbf{k}$ is approximately:

A) $\mathbf{6.02 \times}\mathbf{10}^{\mathbf{- 23\ }}\mathbf{J\ K}^{\mathbf{- 1}}$

B) $\mathbf{1.38 \times}\mathbf{10}^{\mathbf{- 23\ }}\mathbf{J\ K}^{\mathbf{- 1}}$

C) $\mathbf{8.31\ }\mathbf{J\ K}^{\mathbf{- 1}}$

D) $\mathbf{1.38 \times}\mathbf{10}^{\mathbf{23}}\mathbf{\ J\ K}^{\mathbf{- 1}}$

9 / 29

Which equation uses the Boltzmann constant directly?

A) $\mathbf{F = ma}$

B) $\mathbf{E =}\mathbf{mc}^{\mathbf{2}}$

C) $\mathbf{PV = nRT}$

D) $\mathbf{PV = NkT}$

10 / 29

Which relation is dimensionally correct?

A) $\mathbf{R =}\mathbf{kN}_{\mathbf{A}}$

B) $\mathbf{N}_{\mathbf{A}}\mathbf{= Rk}$

C) $\mathbf{k =}$ $\frac{\mathbf{N}_{\mathbf{A}}}{\mathbf{R}}$

D) $\mathbf{R =}$ $\frac{\mathbf{k}}{\mathbf{N}_{\mathbf{A}}}$

11 / 29

Avogadro’s number is approximately:

A) $\mathbf{8.31 \times}\mathbf{10}^{\mathbf{23}}$

B) $\mathbf{1.38 \times}\mathbf{10}^{\mathbf{- 23}}$

C) $\mathbf{6.02 \times}\mathbf{10}^{\mathbf{23}}$

D) $\mathbf{3.0 \times}\mathbf{10}^{\mathbf{8}}$

12 / 29

Boltzmann constant is numerically much smaller than $\mathbf{(R)}$ because:

A) $\mathbf{k}$ depends on pressure.

B) $\mathbf{R}$ is negative.

C) $\mathbf{N}_{\mathbf{A}}$ is a very large number.

D) $\mathbf{N}_{\mathbf{A}}$ is very small.

13 / 29

Boltzmann constant relates temperature to:

A) Electrical charge

B) Molecular energy

C) Volume only

D) Density only

14 / 29

In $\mathbf{PV = NkT}$, increasing $\mathbf{(N)}$ while keeping $\mathbf{(V)}$ and $\mathbf{(T)}$ constant will:

A) Increase pressure

B) Decrease pressure

C) Keep pressure unchanged

D) Make pressure zero

15 / 29

Which quantity has no unit?

A) $\mathbf{k}$

B) $\mathbf{R}$

C) Pressure

D) $\mathbf{N}_{\mathbf{A}}$

16 / 29

If Avogadro’s number were larger, the value of $\mathbf{(k)}$ would be:

A) Unchanged

B) Smaller

C) Larger

D) Zero

17 / 29

The quantity $\mathbf{kT}$ has units of:

A) Energy

B) Temperature

C) Volume

D) Pressure

18 / 29

The Boltzmann constant is most useful when dealing with:

A) Elasticity

B) Planetary motion

C) Individual molecules

D) Electrical circuits

19 / 29

Which equation can be obtained by substituting $\mathbf{R =}\mathbf{kN}_{\mathbf{A}}$ into $\mathbf{PV = nRT\ }$?

A) $\mathbf{PV = RT}$

B) $\mathbf{PV = nkT}$

C) $\mathbf{PV = Nk\ /\ R}$

D) $\mathbf{PV = NkT}$

20 / 29

The physical significance of $\mathbf{(k)}$ is that it:

A) Measures volume directly

B) Measures pressure directly

C) Determines molecular mass

D) Relates mole-scale and particle-scale descriptions of gases

21 / 29

Which statement is correct?

A) $\mathbf{(k)}$ and $\mathbf{(R)}$ have the same numerical value.

B) Both are dimensionless.

C) $\mathbf{(R)}$ is greater than $\mathbf{(k)}$.

D) $\mathbf{(k)}$ is greater than $\mathbf{(R)}$.

22 / 29

The ratio $\frac{\mathbf{R}}{\mathbf{k}}$ equals:

A) Volume

B) Avogadro’s number

C) Pressure

D) Temperature

23 / 29

Why is $\mathbf{PV = NkT}$ preferred in kinetic theory?

A) It avoids temperature.

B) It is valid only for liquids.

C) It uses molecular quantities directly.

D) It ignores molecules.

24 / 29

The unit $\mathbf{JK}^{\mathbf{- 1}}$ suggests that Boltzmann constant relates:

A) Energy to temperature

B) Force to distance

C) Pressure to volume

D) Mass to energy

25 / 29

One mole of gas contains $\mathbf{N}_{\mathbf{A}}$ molecules. Therefore:

A) $\mathbf{N =}\mathbf{kN}_{\mathbf{A}}$

B) $\mathbf{N =}\mathbf{n\ /\ N}_{\mathbf{A}}$

C) $\mathbf{N =}\mathbf{nN}_{\mathbf{A}}$

D) $\mathbf{N =}\mathbf{R\ /\ N}_{\mathbf{A}}$

26 / 29

If $\mathbf{N}_{\mathbf{A}}$ is substituted into $\mathbf{R =}\mathbf{kN}_{\mathbf{A\ }}$, then $\mathbf{R}$ represents:

A) Volume per mole

B) Energy per molecule per Kelvin

C) Pressure per molecule

D) Energy per mole per Kelvin

27 / 29

The numerical value of $\mathbf{(k)}$ indicates that:

A) Temperature has no effect on molecules.

B) Molecules contain infinite energy.

C) Energy changes per molecule are extremely small.

D) Molecular energies are huge.

28 / 29

Which quantity is a fundamental constant of statistical physics?

A) Specific gravity

B) Boltzmann constant

C) Density

D) Young’s modulus

29 / 29

A student forgets Avogadro’s number. Which expression can help recover it?

A) $\mathbf{N}_{\mathbf{A}}\mathbf{=}$ $\frac{\mathbf{R}}{\mathbf{k}}$

B) $\mathbf{N}_{\mathbf{A}}\mathbf{= Rk}$

C) $\mathbf{N}_{\mathbf{A}}\mathbf{=}$ $\frac{\mathbf{k}}{\mathbf{R}}$

D) $\mathbf{N}_{\mathbf{A}}\mathbf{= R + k}$

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