For hydrogen gas, the difference between molar specific heats is given by; \(C_P-C_V=a,\) and for oxygen gas, \(C_P-C_V=b.\) Here, \(C_P\)​ and \(C_V\)​ are molar specific heats expressed in \(\text{J mol}^{-1}\text{K}^{-1}.\) What is the relationship between \(a\) and \(b?\)
1. \(a=16b\)
2. \(b=16a\)
3. \(a=4b\)
4. \(a=b\)

For a gas the difference between the two specific heats is 4150 J/kg K. What is the specific heats at constant volume of gas if the ratio of specific heat is 1.4

1. 8475 J/Kg K                           

2. 5186 J/Kg K

3. 1600 J/Kg K                           

4. 10375 J/Kg K

The specific heat of 1 mole of an ideal gas at constant pressure, ${\mathrm{C}}_{\mathrm{P}}$ and at constant volume $,{\mathrm{C}}_{\mathrm{V}}$ are given. Then-

1. ${\mathrm{C}}_{\mathrm{P}}$ of hydrogen gas is $\frac{5}{2}\mathrm{R}$

2. ${\mathrm{C}}_{\mathrm{V}}$ of hydrogen gas is $\frac{7}{2}\mathrm{R}$

3. ${\mathrm{H}}_2$ has very small values of ${\mathrm{C}}_{\mathrm{P}}$ and ${\mathrm{C}}_{\mathrm{V}}$

4. ${\mathrm{C}}_{\mathrm{P}}-{\mathrm{C}}_{\mathrm{V}}=$ 1.99 cal/mole-K for ${\mathrm{H}}_2$

One mole of ideal monoatomic gas $\left(\mathrm{\gamma }=5/3\right)$ is mixed with one mole of diatomic gas $\left(\mathrm{\gamma }=7/5\right)$. What is $\mathrm{\gamma }$ for the mixture? $\mathrm{\gamma }$ denotes the ratio of specific heat at constant pressure, to that at constant volume

1.  3/2                             

2.  23/15

3.  35/23                         

4.  4/3

A gaseous mixture contains equal number of hydrogen and nitrogen molecules. Specific heat measurements on this mixture at temperatures below 100 K would indicate that the value of $\mathrm{\gamma }$ (ratio of specific heats) for this mixture is

1.  3/2                           

2.  4/3

3.  5/3                           

4.  7/5

One mole of monoatomic gas and three moles of diatomic gas are put together in a container. The molar specific heat $\left(\mathrm{in} \mathrm{J} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1}\right)$ at constant volume is $\left(\mathrm{R}=8.3 \mathrm{J} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1}\right)$

1.  18.7                           

2.  18.9

3.  19.2                           

4.  None of the above

The number of translational degrees of freedom for a diatomic gas is

1.  2                           

2.  3

3.  5                           

4.  6

A gaseous mixture consists of 16g of helium and 16g of oxygen. The ratio $\frac{{\mathrm{C}}_{\mathrm{P}}}{{\mathrm{C}}_{\mathrm{V}}}$ of the mixture is

1.  1.4                       

2.  1.54

3.  1.59                     

4.  1.62

The pressure exerted by the gas on the walls of the container because

1. It loses kinetic energy

2. It sticks with the walls

3. On collision with the walls there is a change in momentum

4. It is accelerated towards the walls

Gas at a pressure ${\mathrm{P}}_0$ is contained in a vessel. If the masses of all the molecules are halved and their speeds are doubled, the resulting pressure P will be equal to

1.  $4{\mathrm{P}}_0$                                 

2.  $2{\mathrm{P}}_0$

3.  ${\mathrm{P}}_0$                                   

4.  $\frac{{\mathrm{P}}_0}{2}$