Choose the correct option related to the specific heat at constant volume $C_V$ -

1. $C_V=\frac{1}{2}fR$           

2. $C_V=\frac{R}{\gamma -1}$

3. $C_V=\frac{C_P}{\gamma }$               

4. All of these

For a gas, $\frac{R}{C_V}=0.67$.  This gas is made up of molecules which are:                                                                   [JIPMER 2001, 02]

1. Diatomic           

2. Mixture of diatomic and polyatomic molecules

3. Monoatomic     

4. Polyatomic

${\mathrm{n}}_1$ mole of monoatomic gas is mixed with ${\mathrm{n}}_2$ mole of diatomic gas such that ${\gamma }_{mix}=1.5$, then:

1. ${\mathrm{n}}_1=2{\mathrm{n}}_2$

2. ${\mathrm{n}}_2=2{\mathrm{n}}_1$

3. $n_1=n_2$

4. $n_1=3n_2$

$\mathrm{Molar}<mspace\; width="1em"></mspace>\mathrm{heat}<mspace\; width="1em"></mspace>\mathrm{capacity}<mspace\; width="1em"></mspace>\mathrm{of}<mspace\; width="1em"></mspace>\mathrm{the}<mspace\; width="1em"></mspace>\mathrm{process}<mspace\; width="1em"></mspace>\mathrm{P}<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>\frac{\mathrm{a}}{\mathrm{T}}<mspace\; width="1em"></mspace>\mathrm{for}<mspace\; width="1em"></mspace>\mathrm{a}<mspace\; width="1em"></mspace>\mathrm{monoatomic}<mspace\; width="1em"></mspace>\mathrm{gas},<mspace\; width="1em"></mspace>\text{'}\mathrm{a}\text{'}<mspace\; width="1em"></mspace>\mathrm{being}<mspace\; width="1em"></mspace>\mathrm{positive}<mspace\; width="1em"></mspace>\mathrm{constant}<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>is-$

1.  $\frac{7}{2}<mspace\; width="1em"></mspace>\mathrm{R}<mspace\; width="1em"></mspace>$

2.  $\frac{5}{2}<mspace\; width="1em"></mspace>\mathrm{R}<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>$

3.  $\frac{3}{2}<mspace\; width="1em"></mspace>\mathrm{R}$

4.  None of these

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

The ratio of two specific heats of gas $C_p/C_v$ for argon is 1.6 and for hydrogen is 1.4. Adiabatic elasticity of argon at pressure P is E. Adiabatic elasticity of hydrogen will also be equal to E at the pressure :

1. P                                       

2. $\frac{8}{7}P$

3. $\frac{7}{8}P$                                   

4. 1.4P

At STP the mass of one litre of air is 1.293 gm. The value of the specific gas constant will be :

1. 0.29 J/K-gm                       

2. 4.2 J/K-gm

3. 8.3 J/K-gm                         

3. 16.5 J/K-gm