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

1.

2.

3.

4.

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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.

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. $\left({\mathrm{T}}_{1}+{\mathrm{T}}_{2}\right)$

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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

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Mean kinetic energy per degree of freedom of gas molecules is

1.

2. $\mathrm{kT}$

3.

4.

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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.

2.

3.

4.

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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.  $2$

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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 ${\mathrm{v}}^{2}$ and the mean square of x component of the velocity of molecules of gas A is ${\mathrm{w}}^{2}$. The ratio is $\frac{{\mathrm{w}}^{2}}{{\mathrm{v}}^{2}}$is

1.  $1$

2.  $2$

3.  $\frac{1}{3}$

4.  $\frac{2}{3}$

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A gas is filled in a cylinder, its temperature is increased by 20% on Kelvin scale and volume is reduced by 10%. How much percentage of the gas will leak out

1. 30%

2. 40%

3. 15%

4. 25%

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The air density at Mount Everest is less than that at the sea level. It is found by mountaineers that for one trip lasting a few hours, the extra oxygen needed by them corresponds to 30,000 cc at sea level (pressure 1 atmosphere, temperature 27°C). Assuming that the temperature around Mount Everest is –73°C and that the oxygen cylinder has capacity of 5.2 litre, the pressure at which ${\mathrm{O}}_{2}$ be filled (at site) in cylinder is

1.  3.86 atm

2.  5.00 atm

3.  5.77 atm

4.  1 atm

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$\frac{1}{2}$ mole of helium gas is contained in a container at S.T.P. The heat energy needed to double the pressure of the gas, keeping the volume constant (specific heat of the gas ) is

1.  3276 J

2.  1638 J

3.  819 J

4.  409.5 J