The kinetic energy of translation of 20 gm of oxygen at 47°C is (molecular wt. of oxygen is 32 gm/mol and R = 8.3 J/mol/K)

1.  2490 joules                   

2.  2490 ergs

3.  830 joules                     

4.  124.5 joules

The kinetic energy of one gram molecules of a gas at standard temperature and pressure: $\left(\mathrm{R}=8.31 \mathrm{J}/\mathrm{mol}-\mathrm{K}\right)$

1.  $0.56\times {10}^4 \mathrm{J}$                           

2.  $1.3\times {10}^2 \mathrm{J}$

3.  $2.7\times {10}^2 \mathrm{J}$                             

4.  $3.4\times {10}^3 \mathrm{J}$

The mean kinetic energy of a gas at 300 K is 100 J. The mean energy of the gas at 450 K is equal to

1.  100 J                             

2.  3000 J

3.  450 J                             

4.  150 J

Read the given statements and decide which is/are correct on the basis of kinetic theory of gases

(I) Energy of one molecule at absolute temperature is zero

(II) r.m.s. speeds of different gases are same at same temperature

(III) For one gram of all ideal gas kinetic energy is same at same temperature

(IV) For one mole of all ideal gases, mean kinetic energy is same at same temperature

1. All are correct                         

2. I and IV are correct

3. IV is correct                           

4. None of these

At 27°C temperature, the kinetic energy of an ideal gas is ${\mathrm{E}}_1$. If the temperature is increased to 327°C, then kinetic energy would be

1.  $2{\mathrm{E}}_1$                               

2.  $\frac{1}{2}{\mathrm{E}}_1$

3.  $\sqrt{2}{\mathrm{E}}_1$                           

4.  $\frac{1}{\sqrt{2}}{\mathrm{E}}_1$

The average kinetic energy of a gas molecule at $27°\mathrm{C}$ is $6.21\times {10}^{-21} \mathrm{J}.$ Its average kinetic energy at $227°\mathrm{C}$ will be

1. $52.2\times {10}^{-21} \mathrm{J}$                           

2. $5.22\times {10}^{-21} \mathrm{J}$

3. $10.35\times {10}^{-21} \mathrm{J}$                         

4. $11.35\times {10}^{-21} \mathrm{J}$

The average translational energy and the r.m.s. speed of molecules in a sample of oxygen gas at 300 K are $6.21\times {10}^{-21} \mathrm{J}$ and 484 m/s respectively. The corresponding values at 600 K are nearly (assuming ideal gas behaviour)

1.  $12.42\times {10}^{21} \mathrm{J}, 968 \mathrm{m}/\mathrm{s}$                     

2.  $8.78\times {10}^{21} \mathrm{J}, 684 \mathrm{m}/\mathrm{s}$

3.  $6.21\times {10}^{21} \mathrm{J}, 968 \mathrm{m}/\mathrm{s}$                       

4.  $12.42\times {10}^{-21} \mathrm{J}, 684 \mathrm{m}/\mathrm{s}$

At 0 K which of the following properties of a gas will be zero

1. Kinetic energy                     

2. Potential energy

3. Vibrational energy               

4. Density

A gas mixture consists of molecules of type 1, 2 and 3, with molar masses ${\mathrm{m}}_1>{\mathrm{m}}_2>{\mathrm{m}}_3. {\mathrm{V}}_{\mathrm{rms}}$ and $\overline{\mathrm{K}}$ are the r.m.s. speed and average kinetic energy of the gases. Which of the following is true

1. ${\left({\mathrm{V}}_{\mathrm{rms}}\right)}_1<{\left({\mathrm{V}}_{\mathrm{rms}}\right)}_2<{\left({\mathrm{V}}_{\mathrm{rms}}\right)}_3 \mathrm{and} {\left(\overline{\mathrm{K}}\right)}_1={\left(\overline{\mathrm{K}}\right)}_2=\left({\overline{\mathrm{K}}}_3\right)$

2. ${\left({\mathrm{V}}_{\mathrm{rms}}\right)}_1={\left({\mathrm{V}}_{\mathrm{rms}}\right)}_2={\left({\mathrm{V}}_{\mathrm{rms}}\right)}_3 \mathrm{and} {\left(\overline{\mathrm{K}}\right)}_1={\left(\overline{\mathrm{K}}\right)}_2>{\left(\overline{\mathrm{K}}\right)}_3$

3. ${\left({\mathrm{V}}_{\mathrm{rms}}\right)}_1>{\left({\mathrm{V}}_{\mathrm{rms}}\right)}_2>{\left({\mathrm{V}}_{\mathrm{rms}}\right)}_3 \mathrm{and} {\left(\overline{\mathrm{K}}\right)}_1<{\left(\overline{\mathrm{K}}\right)}_2>\left({\overline{\mathrm{K}}}_3\right)$

4. ${\left({\mathrm{V}}_{\mathrm{rms}}\right)}_1>{\left({\mathrm{V}}_{\mathrm{rms}}\right)}_2>{\left({\mathrm{V}}_{\mathrm{rms}}\right)}_3 \mathrm{and} {\left(\overline{\mathrm{K}}\right)}_1<{\left(\overline{\mathrm{K}}\right)}_2<{\left(\overline{\mathrm{K}}\right)}_3$

Two ideal gases at absolute temperature ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$ are mixed. There is no loss of energy. The masses of the molecules are ${\mathrm{m}}_1$ and ${\mathrm{m}}_2$ and the number of molecules in the gases are ${\mathrm{n}}_1$ and ${\mathrm{n}}_2$ respectively. The temperature of mixture will be

1. $\frac{{\mathrm{T}}_1+{\mathrm{T}}_2}{2} \mathrm{energy}$                     

2. $\frac{{\mathrm{T}}_1+{\mathrm{T}}_2}{{\mathrm{n}}_1{\mathrm{n}}_2}$

3. $\frac{{\mathrm{n}}_1{\mathrm{T}}_1+{\mathrm{n}}_2{\mathrm{T}}_2}{{\mathrm{n}}_1+{\mathrm{n}}_2}$                         

4. $\left({\mathrm{T}}_1+{\mathrm{T}}_2\right)$