A gas mixture consist of 2 moles of $O_2$ and 4 moles of Ar at temperature T. Neglecting all vibrational modes, the total internal energy of the system is:

1. 4RT 

2. 15RT

3. 9RT

4. 11RT

One mole of an ideal monatomic gas undergoes a process described by the equation $P{V}^3=$ constant. The heat capacity of the gas during this process is:

1. $\frac{3}{2}R$           

2. $\frac{5}{2}R$

3. $2R$             

4. $R$

A given sample of an ideal gas occupies a volume \(V\) at a pressure \(p\) and absolute temperature \(T.\) The mass of each molecule of the gas is \(m.\) Which of the following gives the density of the gas?
1. \(\dfrac{p}{kT}\)
2. \(\dfrac{pm}{kT}\)
3. \(\dfrac{p}{kTV}\)
4. \(mkT\)

The molecules of a given mass of gas have rms velocity of 200 ms^-1 at \(27^{\circ}\mathrm{C}\) and 1.0 x 10⁵ Nm^-2 pressure. When the temperature and pressure of the gas are increased to, respectively, \(127^{\circ}\mathrm{C}\) and 0.05 X 10⁵ Nm^-2, rms velocity of its molecules in ms^-1 will become:
1. 400/√3
2. 100√2/3
3. 100/3 
4.100√2

Two vessels separately contain two ideal gases, \(A\) and \(B\) at the same temperature, the pressure of \(A\) being twice that of \(B.\) Under such conditions, the density of \(A\) is found to be \(1.5\) times the density of \(B.\) The ratio of molecular weight of \(A\) and \(B\) is:
1. \(2/3\)

2. \(3/4\)

3. \(2\)

4. \(1/2\)

A monoatomic gas at a pressure p, having a volume V expands isothermally to a volume 2 V and then adiabatically to a volume 16 V. The final pressure of the gas is: (take  γ=5/3)

1. 64ρ
 

2. 32ρ
 

3. ρ/64
 

4. 16ρ 

The mean free path of molecules of a gas, (radius \(r\)) is inversely proportional to:
1. \(r^3\)
2. \(r^2\)
3. \(r\)
4. \(\sqrt{r}\)

The molar specific heats of an ideal gas at constant pressure and volume are denoted by C_P and C_V respectively. If γ=C_P/C_V and R is the universal gas constant, then CV is equal to

1. 1+γ/1-γ
2. R/(γ-1)
3. (γ-1)/R
4. γR

If ${\mathrm{C}}_{\mathrm{p}}$ and ${\mathrm{C}}_{\mathrm{v}}$ denote the specific heats (per unit mass) of an ideal gas of molecular weight M

1. ${\mathrm{C}}_{\mathrm{p}}-{\mathrm{C}}_{\mathrm{v}}=\frac{\mathrm{R}}{{\mathrm{M}}^2}$                             

2. ${\mathrm{C}}_{\mathrm{p}}-{\mathrm{C}}_{\mathrm{v}}=\mathrm{R}$

3. ${\mathrm{C}}_{\mathrm{p}}-{\mathrm{C}}_{\mathrm{v}}=\frac{\mathrm{R}}{\mathrm{M}}$                               

4. ${\mathrm{C}}_{\mathrm{p}}-{\mathrm{C}}_{\mathrm{v}}=\mathrm{MR}$

At ${10}^{°}C$ the value of the density of a fixed mass of an ideal gas divided by its pressure is x. At ${110}^{°}C$ this ratio is 

1. x

2. $\frac{383}{283}x$

3. $\frac{10}{110}x$

4. $\frac{283}{383}x$