Relating Translational KE and T

Q. Two flasks A and B of equal volume, maintained at 300 K and 700 K contain equal masses of helium and nitrogen gases respectively. What is the ratio of transitional kinetic energy of the gas in flask A to that of flask B?

1. 1 : 3
2. None of these
3. 3 : 1
4. 3 : 49

Q. What is the rms speed of a gas molecule of mass ${10}^{-22}\text{g}$ at room temperature ${27}^{\circ }\text{C}$ according to the kinetic theory of gases?

1. $42.7\text{m/s}$
2. $203.1\text{m/s}$
3. $0.70\text{m/s}$
4. $352.5\text{m/s}$

Q.

What is the average kinetic energy per molecule of the gas?

Q.

In a closed vessel, a gas is heated from 300 K to 600 K; the kinetic energy:

1. Doubles

2. Halves

3. Remains constant

4. None of the above

Q. Helium atom is two times heavier than a hydrogen molecule. At 298 K, the average kinetic energy of a helium atom is:

1. Two times that of a hydrogen molecule
2. Four times that of a hydrogen molecule.
3. Same as that of a hydrogen molecule
4. Half that of a hydrogen molecule

Q.

The average speed at $T_{1}K$ and most probable speed at $T_{2}K$ of $C{O}_2$ gas is $9\times {10}^4$ cm/sec. The values of $T_1$ and $T_2$ are

1. 2143K; 1694K

2. 1726K, 2126K

3. 1684K; 2143K

4. 1684K; 3368K

Q. At what temperature will the total K.E. of 0.3 mol of $He$ be the same as the total K.E. of 0.40 mol of $Ar$ at $400\text{K}$ ?

1. $533\text{K}$
2. $400\text{K}$
3. $346\text{K}$
4. $300\text{K}$

Q.

Molecular velocities of the two gases at the same temperature are $u_1$ and $u_2$. Their masses are $m_1$ and $m_2$ respectively. Which of the following expressions is correct

1. $\frac{m_1}{u_1^2}=\frac{m_2}{u_2^2}$

2. $m_1{u}_1=m_2{u}_2$

3. $\frac{m_1}{u_1}=\frac{m_2}{u_2}$

4. $m_1{u}_1^2=m_2{u}_2^2$

Q. A sample of a gas contains $N_1$ molecules and the total kinetic energy at $-{123}^{\circ }$C is $E_1$ ergs. Another sample of a gas at ${27}^{\circ }$C has a total kinetic energy as $2E_1$ ergs. Assuming gases to be ideal, the number of gas molecules in the second sample will be:

1. $N_1$
2. $N_1/2$
3. $2N_1$
4. $4N_1$

Q. Helium atom is two times heavier than a hydrogen molecule $\left(H_2\right)$. At $298\text{K}$, the average kinetic energy of helium atom is

1. Two times that of a hydrogen molecule
2. Half that of a hydrogen molecule
3. Four times that of a hydrogen molecule
4. Same as that of a hydrogen molecule

Q.

As the temperature is raised from ${20}^{\circ }C$ to ${40}^{\circ }C$. The average kinetic energy of neon atoms changes by a factor of which of the following:

1. $\frac{313}{293}$

2. $\sqrt{\frac{313}{293}}$

3. $\frac{1}{2}$

4. $\frac{2}{1}$

Q. Helium atom is two times heavier than a hydrogen molecule. At 298 K, the average kinetic energy of a helium atom is:

1. Same as that of a hydrogen molecule
2. Half that of a hydrogen molecule
3. Two times that of a hydrogen molecule
4. Four times that of a hydrogen molecule.

Q. $A$ and $B$ are two ideal gases with following parameters:
$\begin{array}{cccc}\text{Gas}& \text{Molecules}& \text{Temperature}& \text{Kinetic energy}\\ A& N_A& -{123}^{\circ }\text{C}& E_A\\ B& N_B& {27}^{\circ }\text{C}& E_B\end{array}$
If $\frac{E_B}{E_A}$ = 2, then $\frac{N_B}{N_A}$ is equal to

1. 4
2. 2
3. 3
4. 1

Q. Which of the following statement(s) is(are) correct regarding the root mean square speed $\left(U_{rms}\right)$ and average translational kinetic energy $\left(E_{av}\right)$ of a molecule in a gas at equilibrium ?

1. $U_{rms}$ is inversely proportional to the square root of its molecular mass
2. $E_{av}$ is doubled when its temperature is increased four times
3. $U_{rms}$ is doubled when its temperature is increased four times
4. $E_{av}$ at a given temperature does not depend on its molecular mass

Q. Helium atom is two times heavier than a hydrogen molecule $\left(H_2\right)$. At $298\text{K}$, the average kinetic energy of helium atom is

1. Two times that of a hydrogen molecule
2. Half that of a hydrogen molecule
3. Four times that of a hydrogen molecule
4. Same as that of a hydrogen molecule

Q. Two flask $A$ and $B$ of equal volumes maintained at temperature $300K$ and $700K$ contains equal mass of $He\left(g\right)$ and $N_2\left(g\right)$ respectively. What is the ratio of translational kinetic energy of gas in flask $A$ to that of flask $B$ ?

1. $1:3$
2. $3:1$
3. $3:49$
4. None of these

Q. What is the rms speed of a gas molecule of mass ${10}^{-22}\text{g}$ at room temperature ${27}^{\circ }\text{C}$ according to the kinetic theory of gases?

1. $42.7\text{m/s}$
2. $203.1\text{m/s}$
3. $0.70\text{m/s}$
4. $352.5\text{m/s}$

Q. During expansion of a gas at a fixed temperature ?

1. There occurs a decrease in pressure
2. There is no change in K.E. of the molecules of gas
3. There occurs a decrease in K.E. of the gaseous molecules
4. There occurs an increase in number of gas molecules

Q. Two flasks $A$ and $B$ of equal volumes are maintained at a temperature of $300\text{K}$ and $700\text{K}$. They contain equal masses of $He\left(g\right)$ and $N_2\left(g\right)$ respectively. What is the ratio of the translational kinetic energy of the gas in flask $A$ to that of flask $B$ ?

1. 1 : 3
2. 3 : 1
3. 3 : 49
4. None of these

Q. Indicate the correct statement for equal volumes of $N_2\left(g\right)$ and $C{O}_2\left(g\right)$ at ${25}^{\circ }\text{C}$ and 1 atm.

1. The average translational kinetic energy per molecule is the same for $N_2$ and $C{O}_2$.
2. The $V_{rms}$ remains same for both $N_2$ and $C{O}_2$.
3. The density of $N_2$ is less than that of $C{O}_2$.
4. The total translational kinetic energy of both $N_2$ and $C{O}_2$ is the same.

Q. Which of the following statement(s) is(are) correct regarding the root mean square speed $\left(U_{rms}\right)$ and average translational kinetic energy $\left(E_{av}\right)$ of a molecule in a gas at equilibrium ?

1. $U_{rms}$ is inversely proportional to the square root of its molecular mass
2. $E_{av}$ is doubled when its temperature is increased four times
3. $U_{rms}$ is doubled when its temperature is increased four times
4. $E_{av}$ at a given temperature does not depend on its molecular mass