Relating Translational KE and T

Q.

The internal energy of an ideal gas depends upon ?

1. only its pressure

2. only its volume

3. only its temperature

4. its pressure and volume

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. 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.

Consider a sample of oxygen behaving like an Ideal gas. At $300\mathrm{K}$, the ratio of root mean square ($\mathrm{rms}$) velocity to the average velocity of a gas molecule will be: (Molecular weight of oxygen is $32\mathrm{g}{\mathrm{mol}}^{-1}$; $\mathrm{R}=8.3\mathrm{J}{\mathrm{K}}^{-1}{\mathrm{mol}}^{-1}$)

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

2. $\sqrt{\frac{8}{3}}$

3. $\sqrt{\frac{3\mathrm{\pi }}{8}}$

4. $\sqrt{\frac{8\mathrm{\pi }}{3}}$

Q.

What is entropy and free energy?

Q.

At the same temperature and pressure, which of the following gas has the highest kinetic energy :

1. 

2. 

3. 

4. 

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

Q. The ratio of the rate of diffusion of helium and methane under the identical conditions of pressure and temperature will be:

1. 4
2. 2
3. 1
4. 0.5

Q. 4 : 1 molar mixture of $He$ and $C{H}_4$ gases is contained in a vessel at 20 bar pressure. Due to a hole in the vessel, the gas mixture leaks out. The ratio of number of moles of $He$ to $C{H}_4$ in the mixture effusing out initially will be:

1. 8 : 1
2. 1 : 8
3. 1 : 4
4. 4 : 1

Q. The ratio of average kinetic energy of $H_2$ and $C{H}_4$ at $27{}^{\circ }C$ will be:

1. 1 : 1
2. 1 : 8
3. 8 : 1
4. 4 : 1

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.

When a machine gun of power P fires n bullets per second, each with kinetic energy E, then P equals

1. nE

2. n/E

3. E/n

4. n²E

Q. The value of Henry’s constant $K_H$ is _____________.

1. greater for gases with lower solubility.
   
2. greater for gases with higher solubility.
   
3. not related to the solubility of gases
4. constant for all gases

Q. 27. Two flasks x and y have capacity 1L and 2L respectively and each of them contains 1 mole of a gas . The temperature of the flasks are so adjusted that average speed of molecules in X is twice as those in Y . The pressure in flasks X would be

Q.

Name the energy which arises due to motion of atoms or molecules in a body. How is this energy affected when the temperature is increased?

Q. Rtae constant k varies with temperature by equation, $logk\left(mi{n}^{-1}\right)=5-\frac{2000}{T\left(K\right)}$, we can conclude :

1. Pre-exponential factor A is $5$
2. $E_a$ is $2000\text{kcal}$
3. Pre-exponential factor A is ${10}^5$
4. $E_a$ is $9.212\text{kcal}$

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.

What happens when entropy reaches maximum?

Q. Photon having wavelength $310\text{nm}$ is used to break the bond of $A_2$ molecule having bond energy $288{\text{kJ mol}}^{–1}$, then percentage of energy of photon converted to the kinetic energy is:
$[hc=12400{\text{evA}}^{\circ },1\text{ev}=96\text{kJ/mol}]$

1. $25\%$
2. $50\%$
3. $75\%$
4. $80\%$

Q. Eight gram each of oxygen and hydrogen at ${27}^{\circ }C$ will have the total kinetic energy in the ratio of x:y. The value of y is

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. 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.

The various steps involved in the process of condensation are given below.

Arrange them in a proper sequence.

(A) Further extraction of heat results in a decrease in the potential energy of molecules, whereas kinetic energy remains constant.

(B) The gas molecules, on cooling, lose heat energy which decreases the kinetic energy as well as the potential energy of the molecules.

(C) An increase in the forces of attraction results in the conversion of state.

(D) A decrease in potential energy leads to an increase in intermolecular forces of attraction.

1. ABCD

2. BADC

3. BACD

4. ABDC

Q. 41. Pure O2 diffuses through an aperture in 224 second , whereas mixture of O2 and another gas containing 80% O2 diffuses from the same in 234 second. What is the molecular mass of gas?

Q.

if the rate of diffusion of a gas is r and its density d, then under similar conditions of pressure and temperature _______.

1. $r\propto d$

2. $r\propto \sqrt{d}$

3. $r\propto \frac{1}{\sqrt{d}}$

4. $r\propto \frac{1}{d}$

Q. The ratio of average kinetic energy of $H_2$ and $C{H}_4$ at $27{}^{\circ }C$ will be:

1. 1 : 1
2. 1 : 8
3. 8 : 1
4. 4 : 1

Q.

A police jeep on a petrol duty on a national highway was moving at a speed of 54 km/hr. In the same direction. It found that a thief was rushing in a car moving at a speed of 126 km/hr. The police sub-inspector fired at the car of the thief with his service revolver with a muzzle speed of 100 m/s. with what speed will the bullet hit the car of a thief?

Q.

At what temperature, the translational kinetic energy of 14 g of nitrogen will be the same as that of 32g of oxygen at 300 K

1. 300 K

2. 600 K

3. 131. 25 K

4. 150 K

Q.

Consider a mixture of $\mathrm{n}$ moles of helium gas and $2\mathrm{n}$ moles of oxygen gas (molecules taken to be rigid) as an ideal gas. Its ($\raisebox{1ex}{${\mathrm{C}}_{\mathrm{p}}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{C}}_{\mathrm{v}}$}\right.$) value will be

1. $\frac{67}{45}$

2. $\frac{40}{27}$

3. $\frac{19}{13}$

4. $\frac{23}{15}$

Q.

At the same temperature and pressure, which of the following gas has the highest kinetic energy :

1. $H_2$

2. $C{H}_4$

3. $O_2$

4. $Alltheabove$