The r.m.s. speed of a certain gas is n at 400K. The temperature at which the r.m.s. speed becomes two times, will be

1.  800 K                         

2.  1600 K

3.  1200 K                       

3.  None of these

A cubical box with porous walls containing an equal number of ${\mathrm{O}}_2$ and ${\mathrm{H}}_2$ molecules is placed in a large evacuated chamber. The entire system is maintained at constant temperature T. The ratio of ${\mathrm{v}}_{\mathrm{rms}}$ of ${\mathrm{O}}_2$ molecules to that of the ${\mathrm{v}}_{\mathrm{rms}}$ of ${\mathrm{H}}_2$ molecules, found in the chamber outside the box after a short interval is

1.  $\frac{1}{2\sqrt{2}}$                             

2.  $\frac{1}{4}$

3.  $\frac{1}{\sqrt{2}}$                               

4.  $\sqrt{2}$

The degrees of freedom of a triatomic gas is

1.  2                                 

2.  4

3.  6                                 

3.  8

The value of C_V for one mole of neon gas is

1.  $\frac{1}{2}\mathrm{R}$                           

2.  $\frac{3}{2}\mathrm{R}$

3.  $\frac{5}{2}\mathrm{R}$                           

4.  $\frac{7}{2}\mathrm{R}$

At constant volume, for different diatomic gases the molar specific heat is

1. Same and 3 cal/mole/°C approximately

2. Exactly equal and its value is 4 cal/mole/°C

3. Will be totally different

4. Approximately equal and its value is 5 cal/mole/°C

At constant volume the specific heat of a gas is $\frac{3\mathrm{R}}{2}$ , then the value of $\text{'}\mathrm{\gamma }\text{'}$ will be

1.  $\frac{3}{2}$                             

2.  $\frac{5}{2}$

3.  $\frac{5}{3}$                             

4.  None of the above

The relation between two specific heats (in cal/mol) of a gas is:
(where \(\text{(J)}\) represents \(1\) Joule)
1. \(C_P-C_V=\dfrac{R}{J}\)
2. \(C_V-C_P=\dfrac{R}{J}\)
3. \(C_P-C_V=R\)
4. \(C_V-C_P=R\)

The specific heat of an ideal gas is:

1.  proportional to $\mathrm{T.}$                     

2.  proportional to T².

3.  proportional to T³.                  

4.  independent of $\mathrm{T.}$

The following sets of values for ${\mathrm{C}}_{\mathrm{V}}$ and ${\mathrm{C}}_{\mathrm{P}}$ of a gas has been reported by different students. The units are cal/gm-mole-K. Which of these sets is most reliable

1. ${\mathrm{C}}_{\mathrm{V}}=3, {\mathrm{C}}_{\mathrm{P}}=5$                                 

2. ${\mathrm{C}}_{\mathrm{V}}=4, {\mathrm{C}}_{\mathrm{P}}=5$

3. ${\mathrm{C}}_{\mathrm{V}}=3, {\mathrm{C}}_{\mathrm{P}}=2$                                 

4. ${\mathrm{C}}_{\mathrm{V}}=3, {\mathrm{C}}_{\mathrm{P}}=4.2$

The specific heats at constant pressure is greater than that of the same gas at constant volume because

1. At constant pressure work is done in expanding the gas

2. At constant volume work is done in expanding the gas

3. The molecular attraction increases more at constant pressure

4. The molecular vibration increases more at constant pressure