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

The molecules of an ideal gas at a certain temperature have

1. Only potential energy

2. Only kinetic energy

3. Potential and kinetic energy both

4. None of the above

The temperature at which the average translational kinetic energy of a molecule is equal to the energy gained by an electron in accelerating from rest through a potential difference of 1 volt is

1.  $4.6\times {10}^3 \mathrm{K}$                 

2.  $11.6\times {10}^3 \mathrm{K}$

3.  $23.2\times {10}^3 \mathrm{K}$               

4.  $7.7\times {10}^3 \mathrm{K}$

The kinetic energy of one mole gas at 300 K temperature, is E. At 400 K temperature kinetic energy is E'. The value of E'/E is

1.  $1.33$                         

2.  $\left(\sqrt{\frac{4}{3}}\right)$

3.  $\frac{16}{9}$                           

4.  $2$

\(N\) molecules each of mass \(m\) of gas \(A\) and \(2N\) molecules each of mass \(2m\) of gas \(B\) are contained in the same vessel at temperature \(T\). The mean square of the velocity of molecules of gas \(B\) is \(v^2\) and the mean square of \(x\) component of the velocity of molecules of gas \(A\) is \(w^2\). The ratio is \(\dfrac{w^2}{v^2}\) is:
1. \(1\)
2. \(2\)
3. \(\dfrac{1}{3}\)
4. \(\dfrac{2}{3}\)