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. p/(kT)        
2. pm / (kT)
3. 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. r³
 

2. r²
 

3. r
 

4. √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. $\frac{283}{383}x$